Notes on the Greek New Testament Day 2 January 2 nd Matthew 2:13-3:6. Works frequently referenced in these notes on Matthew

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Notes on the Greek New Testament Day 2 January 2 nd Matthew 2:13-3:6. Works frequently referenced in these notes on Matthew"

Transcript

1 Notes on the Greek New Testament Day 2 January 2 nd Matthew 2:13-3:6 Works frequently referenced in these notes on Matthew Blomberg, Craig L Jesus and The Gospels, Apollos, Leicester, 1997 Hagner, Donald A Word Biblical Commentary Vols.33a & 33b: Matthew 1-13 & Matthew 14-28, Word Books, Dallas, 1993 & 1995 Morris, Leon The Gospel According to Matthew, Eerdmans, Grand Rapids, 1992 Verses "This pericope is unique to Matthew and is probably drawn from his special source. Two structural features of the pericope are striking. First, the passage divides readily into three separate frames, each ending with an OT quotation: (1) vv 13-15, the dream warning and flight from Egypt (Hos 11:1); (2) vv 16-18, the slaughter of the innocents (Jer 31:15); (3) vv 19-23, the return to Israel and settlement in Nazareth (Isa 11:1?). "Second, there is a remarkable parallelism in the opening of the first and third frames. Apart from the genitive absolutes that begin both frames, we have nearly verbatim agreement in (1) the account of the revelation; (2) the initial imperatives of the angel; and (3) the obedient response of Joseph (which, in each instance, mirrors the angelic commands of the same frame)." Verse 13 Ἀναχωρησάντων δὲ αὐτῶν ἰδοὺ ἄγγελος κυρίου φαίνεται κατʼ ὄναρ τῷ Ἰωσὴφ λέγων Ἐγερθεὶς παράλαβε τὸ παιδίον καὶ τὴν μητέρα αὐτοῦ καὶ φεῦγε εἰς Αἴγυπτον, καὶ ἴσθι ἐκεῖ ἕως ἂν εἴπω σοι μέλλει γὰρ Ἡρῴδης ζητεῖν τὸ παιδίον τοῦ ἀπολέσαι αὐτό. ἀναχωρησάντων Verb, aor act ptc, gen pl φαινω see v.7 The historical present tense adds vividness to the narrative. ἐγειρω raise παράλαβε Verb, aor act imperat, 2 s παραλαμβανω take φευγω flee, run away from ἴσθι Verb, pres imperat, 2 s εἰμι ἐκει there, in that place, to that place ἑως ἀν until This use of ἑως followed by ἀν and the aorist subjunctive is a construction used "to denote that the commencement of an event is dependent upon circumstances." (Baur, Arndt & Gingrich). εἴπω Verb, aor act subj, 1 s λεγω μελλω be going, be about, intend ζητεω seek, search for, look for ἀπολλυμι destroy, kill "This intent is in full accord with what is known of Herod's character and reflects his perception of his threatened status. The verb ἀπολεσαι, 'to destroy,' anticipates its recurrence in the passion narratives (27:20), where, in that instance, it is the chief priests and elders who are the acting subjects." Hagner Verse 14 ὁ δὲ ἐγερθεὶς παρέλαβε τὸ παιδίον καὶ τὴν μητέρα αὐτοῦ νυκτὸς καὶ ἀνεχώρησεν εἰς Αἴγυπτον, Note how Joseph's exact obedience is reflected in the parallel between the words of this and the previous verse. νυξ, νυκτος f night Verse 15 καὶ ἦν ἐκεῖ ἕως τῆς τελευτῆς Ἡρῴδου ἵνα πληρωθῇ τὸ ῥηθὲν ὑπὸ κυρίου διὰ τοῦ προφήτου λέγοντος Ἐξ Αἰγύπτου ἐκάλεσα τὸν υἱόν μου. ἐκει there, in that place τελευτη, ης f death πληρωθῇ Verb, aor pass subj, 3 s πληροω fill, fulfill, bring about ῥηθὲν Verb, aor pass ptc, n nom/acc s λεγω

2 The quotation is from Hos 11:1 with some variants from the LXX (being more in line with the MT). Carson points out that "The NT writers insist that the OT can be rightly interpreted only if the entire revelation is kept in perspective as it is historically unfolded." He goes on to argue for a kind of Israel-Jesus typology in which, "Jesus is the locus of true Israel." Hagner similarly says that πληρωθῇ is to be understood not as suggesting that Hosea wrote of this future event but in terms of typological correspondence. W.D.Davies says that Matthew "sees in the history of Jesus a recapitulation of that of Israel." Hagner comments, "Although Matthew does not capitalise on the Moses- Christ typology, it is certainly not far from his thinking. The one who has come to 'save his people from their sins' (1:21) is the eschatological counterpart to the one who saved his people from the bondage in Egypt... For Matthew, all Israel's history finds its recapitulation in the life of Jesus." Verse 16 Τότε Ἡρῴδης ἰδὼν ὅτι ἐνεπαίχθη ὑπὸ τῶν μάγων ἐθυμώθη λίαν, καὶ ἀποστείλας ἀνεῖλεν πάντας τοὺς παῖδας τοὺς ἐν Βηθλέεμ καὶ ἐν πᾶσι τοῖς ὁρίοις αὐτῆς ἀπὸ διετοῦς καὶ κατωτέρω, κατὰ τὸν χρόνον ὃν ἠκρίβωσεν παρὰ τῶν μάγων. τοτε then, at that time ἰδων Verb, aor act ptc, m nom s ὁραω see, observe, recognise ἐνεπαίχθη Verb, aor pass indic, 3 s ἐμπαιζω trick, deceive The primary meaning of the word is to mock. ἐθυμωθη Verb, aor pass dep indic, 3 s θυμοομαι be furious λιαν adv exceedingly, greatly ἀποστελλω send, send out ἀνεῖλεν Verb, aor act indic, 3 s ἀναιρεω do away with, kill παις, παιδος m & f servant, child ὁριον, ου n neighbourhood, vicinity διετης, ες two years old κατωτερω adv. under, less (of age) χρονος, ου m time, period of time ἀκριβοω see v.7 Herod "gives himself an extra measure both of temporal and geographical assurance." This would probably have amounted to about 20 children. Verse 17 τότε ἐπληρώθη τὸ ῥηθὲν διὰ Ἰερεμίου τοῦ προφήτου λέγοντος τοτε see v.16 πληροω see v.15 ῥηθὲν see v.15 Verse 18 Φωνὴ ἐν Ῥαμὰ ἠκούσθη, κλαυθμὸς καὶ ὀδυρμὸς πολύς Ῥαχὴλ κλαίουσα τὰ τέκνα αὐτῆς, καὶ οὐκ ἤθελεν παρακληθῆναι ὅτι οὐκ εἰσίν. The words are from Jer. 31:15 (LXX 38:15), with significant differences from the LXX. Rachel is viewed figuratively as the mother of the nation. κλαυθμος, ου m bitter crying, wailing ὀδυρμος, ου m mourning, grieving TR C D L W f 13 and syr s,c, among others, include a third word, θρηνος (a synonym of the other two), this apparently by way of harmonisation with the text of LXX. πολυς, πολλη, πολυ gen πολλου, ης, ου much κλαιω weep, cry; trans weep for τεκνον, ου n child ἤθελεν Verb, imperf act indic, 3 s θελω wish, will παρακληθῆναι Verb, aor pass infin παρακαλεω encourage, comfort "Nothing can alter the fact of the Exile and nothing can alter the fact of the killings at Bethlehem. Thus the grief remains. Yet we should add that Jeremiah's prophecy goes on to the note of hope (Jer 31:17) and to the making of a new covenant (Jer 31:31-34)." Hagner, recalling his earlier statement, "For Matthew, all Israel's history finds its recapitulation in the life of Jesus", says that this is "further substantiated by Matthew's introduction of an exilic motif in Jeremiah's reference to Rachel's weeping for her children... The story of Jesus, even at its beginning, sums up and presents the ultimate significance of all that has preceded, both good and evil. This is especially true of the major events such as the slavery/exodus and the exile/return which are already related in later writings of the OT as being theologically of one fabric... In Matthew's perspective, Jesus is understood as summarising the whole experience of Israel as well as bringing it to fulfilment. Every strand of hope and trial in the OT is woven together in the eschatological appearance of the Promised One." Verse 19 Τελευτήσαντος δὲ τοῦ Ἡρῴδου ἰδοὺ ἄγγελος κυρίου φαίνεται κατʼ ὄναρ τῷ Ἰωσὴφ ἐν Αἰγύπτῳ τελευταω die φαινω see v.7

3 Verse 20 λέγων Ἐγερθεὶς παράλαβε τὸ παιδίον καὶ τὴν μητέρα αὐτοῦ καὶ πορεύου εἰς γῆν Ἰσραήλ, τεθνήκασιν γὰρ οἱ ζητοῦντες τὴν ψυχὴν τοῦ παιδίου. Compare the words of command in v.13 πορευομαι go, travel γη, γης f earth, land An obvious echo of the Exodus narrative. τεθνήκασιν Verb, perf act indic, 3 pl θνησκω die; perf be dead ζητοῦντες Verb, pres act ptc, m nom s ζητεω see v.13 ψυχη, ης f inmost being, life, 'soul' Cf. Exod 4:19. Verse 21 ὁ δὲ ἐγερθεὶς παρέλαβε τὸ παιδίον καὶ τὴν μητέρα αὐτοῦ καὶ εἰσῆλθεν εἰς γῆν Ἰσραήλ. εἰσηλθεν Verb, aor act indic, 3 s εἰσερχομαι enter, go in, come in The echo of the words of command in v.20 underlines Joseph's careful obedience. Verse 22 ἀκούσας δὲ ὅτι Ἀρχέλαος βασιλεύει τῆς Ἰουδαίας ἀντὶ τοῦ πατρὸς αὐτοῦ Ἡρῴδου ἐφοβήθη ἐκεῖ ἀπελθεῖν χρηματισθεὶς δὲ κατʼ ὄναρ ἀνεχώρησεν εἰς τὰ μέρη τῆς Γαλιλαίας, βασιλευω rule, reign ἀντι prep with gen in place of πατηρ, πατρος m father ἐφοβήθη Verb, aor pass dep indic, 3 s φοβεομαι fear, be afraid (of) ἐκει there, in that place χρηματισθεὶς Verb, aor pass ptc, m nom s χρηματιζω warn, direct, instruct μερος, ους n part, piece, region "Luke tells us that they had lived in Nazareth before going to Bethlehem (Luke 1:26; 2:4). Perhaps they would have liked to make their home in the city of David, especially in view of the circumstances attending Jesus' birth. But there was a difficulty arising from the fact that the area was now ruled by Archelaus... He was noted for his cruelty even in an age when cruel men were not scarce, so it is not surprising that Joseph feared to settle in this man's dominions." Hagner comments, "To be sure, another son of Herod, Herod Antipas, ruled as ethnarch over Galilee and Perea. But he was a more tolerant ruler, and Galilee in his day became known for revolutionary sentiments that would never have been tolerated by his father." "The mention of Galilee is theologically important for Matthew as we shall see in 4: There he again writes, now of Jesus, ἀνεχωρησεν εἰς την Γαλιλαιαν, 'he departed into Galilee' (4:12). It is in Galilee that he inaugurates his ministry in fulfilment of Isa 9:1 (which Matthew then cites). Galilee's large population of Gentiles symbolises the universal significance Matthew sees in Jesus." Verse 23 καὶ ἐλθὼν κατῴκησεν εἰς πόλιν λεγομένην Ναζαρέτ, ὅπως πληρωθῇ τὸ ῥηθὲν διὰ τῶν προφητῶν ὅτι Ναζωραῖος κληθήσεται. κατοικεω live, settle πολις, εως f city, town The alternative spelling Ναζαρεθ is found in a number of MSS. ὁπως (or ὁπως ἀν) that, in order that πληρωθῇ see v.15 for this and the following words Ναζωραιος, ου m inhabitant of Nazareth, Nazarene

4 Note the untypically general nature of the reference, 'what was spoken through the prophets...' Morris writes, "It appears that Matthew is drawing attention to the thrust of Old Testament prophecy about Christ rather than to one passage. Jesus went to Galilee so that what was written about him in the prophets could be fulfilled, and we see this in his being called a Nazarene, a citizen of an obscure and unimportant town. Had he been known as 'Jesus of Bethlehem' he would have had the aura of one who came from a royal city; there would have been overtones of messianic majesty. But 'Jesus the Nazarene' carries with it overtones of contempt. We are to understand the prophets as pointing to one who would be despised and rejected and Jesus as fulfilling this by being connected with obscure Nazareth." Others have suggested that Matthew alludes to: i) Jesus as a Nazirite (cf. Num 6:1-6) Sanders, Schweizer; ii) The messianic prophecy concerning the Branch (Hebrew neser cf. Is 11:1) Black, Stendahl, Matthew 3:1-12 "The background to this passage is to be found in the expectation of Jewish apocalyptic (cf. Dan 2:44; 7:14-27). John, the appointed forerunner, announces that the promised kingdom is on the verge of dawning. The promises of a new, golden age are about to be realised. This means not only the experience of blessing for the righteous but the overthrow and judgment of the wicked, the enemies of Israel. To a larger extent, therefore, John's announcement is readily intelligible to his listeners, who eagerly await their God to act. Extrabiblical evidence (e.g., Pss Sol ) indicates that such expectations were at a high level in first century Palestine. At the same time, John's message contains some surprises." Verse 1 Ἐν δὲ ταῖς ἡμέραις ἐκείναις παραγίνεται Ἰωάννης ὁ βαπτιστὴς κηρύσσων ἐν τῇ ἐρήμῳ τῆς Ἰουδαίας ἐκεινος, η, ο demonstrative adj. that, those It is not intended to imply that these events closely followed those surrounding Jesus birth. This phrase should probably be understood to mean "'in those crucial days' or 'in that critical time.'" Hill. παραγινομαι come, arrive, appear βαπτιστης, ου m Baptist, baptiser κηρυσσω preach, proclaim "The word properly means something like "make known by a herald" and indicates a message given by authority to the proclaimer, not a free composition of his own." ἐρημος, ου f deserted place, uninhabited region "This particular wilderness is that of Judea, the country from the watershed in the Judean hills eastward to the river Jordan. Its rainfall is light and its slopes steep; thus it offers little scope for agriculture. John will have been located toward the south of the area, where there were fords and people could come out to meet him." Verse 2 καὶ λέγων Μετανοεῖτε, ἤγγικεν γὰρ ἡ βασιλεία τῶν οὐρανῶν. μετανοεω repent, have a change of heart, turn from one's sins "In preaching repentance, John takes up the message of the prophets. In anticipation of God's activity which involves judgment as well as redemption, there can only be one clarion call: to turn, to return to the God of Israel." This distinctive of John's preaching is also the note with which Jesus began his own ministry (Matt 4:17). Hagner comments, "John and Jesus therefore stand in continuity, and the message of John to the Jews is equally a message to Matthew's church." ἤγγικεν Verb, perf act indic, 3 s ἐγγιζω approach, draw near οὐρανος, ου m heaven Matthew's 'kingdom of heaven' is equivalent to 'kingdom of God' in the other Gospels. Matthew favours this phrase (33 occurrences) and it is used only by him in the NT. Morris concurs that it is "a Jewish expression with the word 'God' avoided out of motives of reverence" but then goes on to indicate something of the distinctive character of the kingdom signified by this term: it is the reign of God which is already exercised in heaven but which is being extended to earth. The kingdom is closely connected with the person of Jesus hence its being near. Verse 3 οὗτος γάρ ἐστιν ὁ ῥηθεὶς διὰ Ἠσαΐου τοῦ προφήτου λέγοντος Φωνὴ βοῶντος ἐν τῇ ἐρήμῳ Ἑτοιμάσατε τὴν ὁδὸν κυρίου, εὐθείας ποιεῖτε τὰς τρίβους αὐτοῦ. ῥηθεὶς Verb, aor pass ptc, m nom s λεγω The quotation is from Is 40:3. Matthew follows the LXX verbatim except for the last word αὐτου which in LXX is του θεου ἡμων.

5 φωνη, ης f voice, noise It is the message rather than the messenger which is important. βοαω call, cry out, shout ἐν τῇ ἐρήμω Hagner comments, In the parallelism of the Hebrew text, [this] is part of the message of the voice; that is, the preparation is to be made in the wildernss... But by either understanding, John fulfills the passage. His was a voice crying in the wilderness, and it was in the wilderness that he offered the baptism of preparation (cf. v 1). John s message of repentance and his call to righteousness correspond to preparing the way of the Promised One or, using Isaiah s metaphor, making his paths straight. ἑτοιμαζω prepare, make ready ὁδος, ου f way, path, road "'The Lord' refers in Isaiah to Yahweh, but the Baptist is applying the passage to Jesus. When Matthew records this use of Scripture he is revealing something of his Christology." εὐθυς, εια, υ straight, level τριβος, ου f path, pathway Verse 4 αὐτὸς δὲ ὁ Ἰωάννης εἶχεν τὸ ἔνδυμα αὐτοῦ ἀπὸ τριχῶν καμήλου καὶ ζώνην δερματίνην περὶ τὴν ὀσφὺν αὐτοῦ, ἡ δὲ τροφὴ ἦν αὐτοῦ ἀκρίδες καὶ μέλι ἄγριον. εἶχεν Verb, imperf act indic, 3 s ἐχω ἐνδυμα, τος n clothing, garment τριχῶν Noun, gen pl θριξ, τριχος f hair καμηλος, ου m & f camel ζωνη, ης f belt δερματινος, η, ον of leather ὀσφυς, υος f waist Cf. 2 Kings 1:8 for similar clothing worn by Elijah. "John symbolises the breaking of the centuries of prophetic silence recognised by the Jews themselves (cf. 1 Macc 4:46; 9:27; 14:41). Here then is a new thing: a voice from God out of the silence, self authenticating by its power and message, as well as by its unusual mediator. Prophecy appears again in the midst of Israel, the people of God." τροφη, ης f food, nourishment ἀκρις, ιδος f locust, grasshopper μελι, ιτος n honey ἀγριος, α, ον wild "The picture we get is of a man who lived simply. His clothing was far from splendid or elaborate, and his food such as could be obtained from the wild." Verse 5 τότε ἐξεπορεύετο πρὸς αὐτὸν Ἱεροσόλυμα καὶ πᾶσα ἡ Ἰουδαία καὶ πᾶσα ἡ περίχωρος τοῦ Ἰορδάνου, τοτε then, at that time ἐκπορευομαι go or come out περιχωρος, ου f surrounding region, neighbourhood Ἰορδανης, ου m Jordan River "The forerunner... appears to enjoy as much or even more success than will the one whom he precedes." Verse 6 καὶ ἐβαπτίζοντο ἐν τῷ Ἰορδάνῃ ποταμῷ ὑπʼ αὐτοῦ ἐξομολογούμενοι τὰς ἁμαρτίας αὐτῶν. βαπτιζω baptise, wash ποταμος, ου m river, stream "Since Christians are familiar with baptism only as a religious ceremony, we are apt to miss some of the meaning. But the verb means 'dip, plunge' and in the passive, 'be drowned'; it is used of ships in the sense 'sink'... We should not miss the significance of this violent imagery. Baptism signifies death to a whole way of life (cf. Rom 6:3). The Jews employed baptism in admitting Gentiles as proselytes, but the sting in John's practice was that he applied it to Jews!" "Remarkably, Jews came to submit themselves to a rite that for them had the association of the initiation of gentile proselytes into Judaism. But the announcement of the imminent end of the age no doubt seemed to justify confession of sins and the cleansing symbolism of the baptism." ἐξομολογεω agree; midd confess, acknowledge ἁμαρτια, ας f sin "When people really repent they say so."

Matthew 2. LGNT -May 26, 2019 Page 1. Book Chapter Verse. Word # in Matt. Interlinear English. Numeric value. # of words. # of letters.

Matthew 2. LGNT -May 26, 2019 Page 1. Book Chapter Verse. Word # in Matt. Interlinear English. Numeric value. # of words. # of letters. Book Chapter Verse Interlinear English Word # in Matt Greek # of letters # of words Numeric value 010201 00437 ΤΟΥ 3 770 010201 and 00438 ΔΕ 2 9 010201 Jesus 00439 ΙΗΣΟΥ 5 688 010201 having been born 00440

Διαβάστε περισσότερα

derivation of the Laplacian from rectangular to spherical coordinates

derivation of the Laplacian from rectangular to spherical coordinates derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used

Διαβάστε περισσότερα

Chapter 2 * * * * * * * Introduction to Verbs * * * * * * *

Chapter 2 * * * * * * * Introduction to Verbs * * * * * * * Chapter 2 * * * * * * * Introduction to Verbs * * * * * * * In the first chapter, we practiced the skill of reading Greek words. Now we want to try to understand some parts of what we read. There are a

Διαβάστε περισσότερα

Notes on the Greek New Testament Week 131 Matthew 2:1-3:6

Notes on the Greek New Testament Week 131 Matthew 2:1-3:6 Notes on the Greek New Testament Week 131 Matthew 2:1-3:6 Day 651: Matthew 2:1-6 Matthew 2:1-12 "In this narrative the Jews and their king are ranged against the infant Jesus, but the Gentiles do him homage."

Διαβάστε περισσότερα

2 Composition. Invertible Mappings

2 Composition. Invertible Mappings Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,

Διαβάστε περισσότερα

Section 8.3 Trigonometric Equations

Section 8.3 Trigonometric Equations 99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.

Διαβάστε περισσότερα

Adjectives. Describing the Qualities of Things. A lesson for the Paideia web-app Ian W. Scott, 2015

Adjectives. Describing the Qualities of Things. A lesson for the Paideia web-app Ian W. Scott, 2015 Adjectives Describing the Qualities of Things A lesson for the Paideia web-app Ian W. Scott, 2015 Getting Started with Adjectives It's hard to say much using only nouns and pronouns Simon is a father.

Διαβάστε περισσότερα

LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV. 18 February 2014

LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV. 18 February 2014 LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV 18 February 2014 Slowly/quietly Clear/clearly Clean Quickly/quick/fast Hurry (in a hurry) Driver Attention/caution/notice/care Dance Σιγά Καθαρά Καθαρός/η/ο

Διαβάστε περισσότερα

WEEK 21. The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1

WEEK 21. The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1 WEEK 21 The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1 I. The Feast of Firstfruits signifies the resurrected Christ as the firstfruits for our enjoyment as

Διαβάστε περισσότερα

Chapter 29. Adjectival Participle

Chapter 29. Adjectival Participle Chapter 29 Adjectival Participle Overview (29.3-5) Definition: Verbal adjective Function: they may function adverbially or adjectivally Forms: No new forms because adverbial and adjectival participles

Διαβάστε περισσότερα

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =

Διαβάστε περισσότερα

Finite Field Problems: Solutions

Finite Field Problems: Solutions Finite Field Problems: Solutions 1. Let f = x 2 +1 Z 11 [x] and let F = Z 11 [x]/(f), a field. Let Solution: F =11 2 = 121, so F = 121 1 = 120. The possible orders are the divisors of 120. Solution: The

Διαβάστε περισσότερα

Writing for A class. Describe yourself Topic 1: Write your name, your nationality, your hobby, your pet. Write where you live.

Writing for A class. Describe yourself Topic 1: Write your name, your nationality, your hobby, your pet. Write where you live. Topic 1: Describe yourself Write your name, your nationality, your hobby, your pet. Write where you live. Χρησιμοποίησε το and. WRITE your paragraph in 40-60 words... 1 Topic 2: Describe your room Χρησιμοποίησε

Διαβάστε περισσότερα

EE512: Error Control Coding

EE512: Error Control Coding EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3

Διαβάστε περισσότερα

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού)

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Προσδοκώμενα αποτελέσματα Περιεχόμενο Ενδεικτικές δραστηριότητες

Διαβάστε περισσότερα

14 Lesson 2: The Omega Verb - Present Tense

14 Lesson 2: The Omega Verb - Present Tense Lesson 2: The Omega Verb - Present Tense Day one I. Word Study and Grammar 1. Most Greek verbs end in in the first person singular. 2. The present tense is formed by adding endings to the present stem.

Διαβάστε περισσότερα

ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α. Διαβάστε τις ειδήσεις και εν συνεχεία σημειώστε. Οπτική γωνία είδησης 1:.

ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α.  Διαβάστε τις ειδήσεις και εν συνεχεία σημειώστε. Οπτική γωνία είδησης 1:. ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α 2 ειδήσεις από ελληνικές εφημερίδες: 1. Τα Νέα, 13-4-2010, Σε ανθρώπινο λάθος αποδίδουν τη συντριβή του αεροσκάφους, http://www.tanea.gr/default.asp?pid=2&artid=4569526&ct=2 2. Τα Νέα,

Διαβάστε περισσότερα

Matthew saying ΛΕΓΩΝ repent ΜΕΤΑΝΟΕΙΤΕ

Matthew saying ΛΕΓΩΝ repent ΜΕΤΑΝΟΕΙΤΕ Book Chapter Verse Interlinear English Word # in Matt Greek # of letters # of words Numeric value 010301 [and] in 00894 ΕΝ 2 55 010301 00895 ΔΕ 2 9 010301 the 00896 ΤΑΙΣ 4 511 010301 days 00897 ΗΜΕΡΑΙΣ

Διαβάστε περισσότερα

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch: HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying

Διαβάστε περισσότερα

Every set of first-order formulas is equivalent to an independent set

Every set of first-order formulas is equivalent to an independent set Every set of first-order formulas is equivalent to an independent set May 6, 2008 Abstract A set of first-order formulas, whatever the cardinality of the set of symbols, is equivalent to an independent

Διαβάστε περισσότερα

Strain gauge and rosettes

Strain gauge and rosettes Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ ΝΟΜΙΚΟ ΚΑΙ ΘΕΣΜΙΚΟ ΦΟΡΟΛΟΓΙΚΟ ΠΛΑΙΣΙΟ ΚΤΗΣΗΣ ΚΑΙ ΕΚΜΕΤΑΛΛΕΥΣΗΣ ΠΛΟΙΟΥ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ που υποβλήθηκε στο

Διαβάστε περισσότερα

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β 3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle

Διαβάστε περισσότερα

7 Present PERFECT Simple. 8 Present PERFECT Continuous. 9 Past PERFECT Simple. 10 Past PERFECT Continuous. 11 Future PERFECT Simple

7 Present PERFECT Simple. 8 Present PERFECT Continuous. 9 Past PERFECT Simple. 10 Past PERFECT Continuous. 11 Future PERFECT Simple A/ Ονόματα και ένα παράδειγμα 1 Present Simple 7 Present PERFECT Simple 2 Present Continuous 8 Present PERFECT Continuous 3 Past Simple (+ used to) 9 Past PERFECT Simple she eats she is eating she ate

Διαβάστε περισσότερα

Συντακτικές λειτουργίες

Συντακτικές λειτουργίες 2 Συντακτικές λειτουργίες (Syntactic functions) A. Πτώσεις και συντακτικές λειτουργίες (Cases and syntactic functions) The subject can be identified by asking ποιος (who) or τι (what) the sentence is about.

Διαβάστε περισσότερα

Right Rear Door. Let's now finish the door hinge saga with the right rear door

Right Rear Door. Let's now finish the door hinge saga with the right rear door Right Rear Door Let's now finish the door hinge saga with the right rear door You may have been already guessed my steps, so there is not much to describe in detail. Old upper one file:///c /Documents

Διαβάστε περισσότερα

LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV. 10 December 2013

LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV. 10 December 2013 LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV 10 December 2013 I get up/i stand up I wash myself I shave myself I comb myself I dress myself Once (one time) Twice (two times) Three times Salary/wage/pay Alone/only

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 9: Inversion Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons εκτός

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο

Διαβάστε περισσότερα

C.S. 430 Assignment 6, Sample Solutions

C.S. 430 Assignment 6, Sample Solutions C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order

Διαβάστε περισσότερα

Math 6 SL Probability Distributions Practice Test Mark Scheme

Math 6 SL Probability Distributions Practice Test Mark Scheme Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry

Διαβάστε περισσότερα

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013 Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering

Διαβάστε περισσότερα

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ. Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action

Διαβάστε περισσότερα

4.6 Autoregressive Moving Average Model ARMA(1,1)

4.6 Autoregressive Moving Average Model ARMA(1,1) 84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this

Διαβάστε περισσότερα

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required) Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts

Διαβάστε περισσότερα

The Accusative Case. A Target for the Action. A lesson for the Paideia web-app Ian W. Scott, 2015

The Accusative Case. A Target for the Action. A lesson for the Paideia web-app Ian W. Scott, 2015 The Accusative Case A Target for the Action A lesson for the Paideia web-app Ian W. Scott, 2015 The Accusative Case So far we've seen three noun cases Nominative Genitive Vocative We need one more case

Διαβάστε περισσότερα

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι She selects the option. Jenny starts with the al listing. This has employees listed within She drills down through the employee. The inferred ER sttricture relates this to the redcords in the databasee

Διαβάστε περισσότερα

Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951)

Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951) 1 Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951) Αναγνώσματα από το βιβλίο Η Απόλαυση της Μουσικής (Machlis, Forney), για τους μαθητές που θα μελετήσουν το έργο: «Ο Σαίνμπεργκ

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 4: English a Language of Economy Το περιεχόμενο του μαθήματος διατίθεται με άδεια

Διαβάστε περισσότερα

Croy Lessons Participles

Croy Lessons Participles A Croy Lessons 18-20 Participles Aorist (Act/Mid/Dep Dep) ) Participles Adjectival and Substantive Ω STEM + TENSE + THEME + PTCP CODE + ENDING PARTICIPLE CODES CASE ENDINGS ντ - masc and neut active (and

Διαβάστε περισσότερα

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr 9.9 #. Area inside the oval limaçon r = + cos. To graph, start with = so r =. Compute d = sin. Interesting points are where d vanishes, or at =,,, etc. For these values of we compute r:,,, and the values

Διαβάστε περισσότερα

Statistical Inference I Locally most powerful tests

Statistical Inference I Locally most powerful tests Statistical Inference I Locally most powerful tests Shirsendu Mukherjee Department of Statistics, Asutosh College, Kolkata, India. shirsendu st@yahoo.co.in So far we have treated the testing of one-sided

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 11: The Unreal Past Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons

Διαβάστε περισσότερα

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds!

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds! MTH U341 urface Integrals, tokes theorem, the divergence theorem To be turned in Wed., Dec. 1. 1. Let be the sphere of radius a, x 2 + y 2 + z 2 a 2. a. Use spherical coordinates (with ρ a) to parametrize.

Διαβάστε περισσότερα

Démographie spatiale/spatial Demography

Démographie spatiale/spatial Demography ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΙΑΣ Démographie spatiale/spatial Demography Session 1: Introduction to spatial demography Basic concepts Michail Agorastakis Department of Planning & Regional Development Άδειες Χρήσης

Διαβάστε περισσότερα

Code Breaker. TEACHER s NOTES

Code Breaker. TEACHER s NOTES TEACHER s NOTES Time: 50 minutes Learning Outcomes: To relate the genetic code to the assembly of proteins To summarize factors that lead to different types of mutations To distinguish among positive,

Διαβάστε περισσότερα

Homework 3 Solutions

Homework 3 Solutions Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For

Διαβάστε περισσότερα

Croy Lesson 18. First Declension. THIRD Declension. Second Declension. SINGULAR PLURAL NOM -α / -η [-ης]* -αι. GEN -ας / -ης [-ου]* -ων

Croy Lesson 18. First Declension. THIRD Declension. Second Declension. SINGULAR PLURAL NOM -α / -η [-ης]* -αι. GEN -ας / -ης [-ου]* -ων Croy Lesson 18 First Declension SINGULAR PLURAL NOM -α / -η [-ης]* -αι GEN -ας / -ης [-ου]* -ων DAT -ᾳ / -ῃ -αις ACC -αν / -ην -ας VOC -α / -η -αι *Masculine Nouns of First Declension Second Declension

Διαβάστε περισσότερα

Approximation of distance between locations on earth given by latitude and longitude

Approximation of distance between locations on earth given by latitude and longitude Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth

Διαβάστε περισσότερα

Example Sheet 3 Solutions

Example Sheet 3 Solutions Example Sheet 3 Solutions. i Regular Sturm-Liouville. ii Singular Sturm-Liouville mixed boundary conditions. iii Not Sturm-Liouville ODE is not in Sturm-Liouville form. iv Regular Sturm-Liouville note

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

Συστήματα Διαχείρισης Βάσεων Δεδομένων

Συστήματα Διαχείρισης Βάσεων Δεδομένων ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Συστήματα Διαχείρισης Βάσεων Δεδομένων Φροντιστήριο 9: Transactions - part 1 Δημήτρης Πλεξουσάκης Τμήμα Επιστήμης Υπολογιστών Tutorial on Undo, Redo and Undo/Redo

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1 Conceptual Questions. State a Basic identity and then verify it. a) Identity: Solution: One identity is cscθ) = sinθ) Practice Exam b) Verification: Solution: Given the point of intersection x, y) of the

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΨΥΧΟΛΟΓΙΚΕΣ ΕΠΙΠΤΩΣΕΙΣ ΣΕ ΓΥΝΑΙΚΕΣ ΜΕΤΑ ΑΠΟ ΜΑΣΤΕΚΤΟΜΗ ΓΕΩΡΓΙΑ ΤΡΙΣΟΚΚΑ Λευκωσία 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή

Διαβάστε περισσότερα

LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26. 18 November 2014

LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26. 18 November 2014 LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26 18 November 2014 But Weekend I love The song I sing I smile I laugh Greek (thing) Greek(people) Greek (man) αλλά (το) Σαββατοκύριακο αγαπώ (το) τραγούδι τραγουδώ

Διαβάστε περισσότερα

ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ

ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ Ενότητα 1β: Principles of PS Ιφιγένεια Μαχίλη Τμήμα Οικονομικών Επιστημών Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης

Διαβάστε περισσότερα

I haven t fully accepted the idea of growing older

I haven t fully accepted the idea of growing older I haven t fully accepted the idea of growing older 1 Peter Authorship Questions Πέτρος ἀπόστολος Ἰησοῦ Χριστοῦ ἐκλεκτοῖς παρεπιδήμοις διασπορᾶς Πόντου, Γαλατίας, Καππαδοκίας, Ἀσίας 1 Peter Authorship

Διαβάστε περισσότερα

TMA4115 Matematikk 3

TMA4115 Matematikk 3 TMA4115 Matematikk 3 Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet Trondheim Spring 2010 Lecture 12: Mathematics Marvellous Matrices Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet

Διαβάστε περισσότερα

the total number of electrons passing through the lamp.

the total number of electrons passing through the lamp. 1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy

Διαβάστε περισσότερα

Assalamu `alaikum wr. wb.

Assalamu `alaikum wr. wb. LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011 Διάρκεια Διαγωνισμού: 3 ώρες Απαντήστε όλες τις ερωτήσεις Μέγιστο Βάρος (20 Μονάδες) Δίνεται ένα σύνολο από N σφαιρίδια τα οποία δεν έχουν όλα το ίδιο βάρος μεταξύ τους και ένα κουτί που αντέχει μέχρι

Διαβάστε περισσότερα

6.1. Dirac Equation. Hamiltonian. Dirac Eq.

6.1. Dirac Equation. Hamiltonian. Dirac Eq. 6.1. Dirac Equation Ref: M.Kaku, Quantum Field Theory, Oxford Univ Press (1993) η μν = η μν = diag(1, -1, -1, -1) p 0 = p 0 p = p i = -p i p μ p μ = p 0 p 0 + p i p i = E c 2 - p 2 = (m c) 2 H = c p 2

Διαβάστε περισσότερα

Srednicki Chapter 55

Srednicki Chapter 55 Srednicki Chapter 55 QFT Problems & Solutions A. George August 3, 03 Srednicki 55.. Use equations 55.3-55.0 and A i, A j ] = Π i, Π j ] = 0 (at equal times) to verify equations 55.-55.3. This is our third

Διαβάστε περισσότερα

Ρηματική άποψη. (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect)

Ρηματική άποψη. (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect) 15 Ρηματική άποψη (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect) imperfective perfective Verb forms in Modern Greek are based either on the imperfective or the perfective

Διαβάστε περισσότερα

Τμήμα Πολιτικών και Δομικών Έργων

Τμήμα Πολιτικών και Δομικών Έργων Τμήμα Πολιτικών και Δομικών Έργων Πτυχιακή Εργασία: Τοπογραφικό διάγραμμα σε ηλεκτρονική μορφή κεντρικού λιμένα Κέρκυρας και κτιρίου νέου επιβατικού σταθμού σε τρισδιάστατη μορφή και σχεδίαση με AutoCAD

Διαβάστε περισσότερα

Επιβλέπουσα Καθηγήτρια: ΣΟΦΙΑ ΑΡΑΒΟΥ ΠΑΠΑΔΑΤΟΥ

Επιβλέπουσα Καθηγήτρια: ΣΟΦΙΑ ΑΡΑΒΟΥ ΠΑΠΑΔΑΤΟΥ EΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΕΚΠΑΙΔΕΥΤΙΚΟ ΤΕΧΝΟΛΟΓΙΚΟ ΙΔΡΥΜΑ ΤΕΙ ΙΟΝΙΩΝ ΝΗΣΩΝ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ Ταχ. Δ/νση : Λεωφ. Αντ.Τρίτση, Αργοστόλι Κεφαλληνίας Τ.Κ. 28 100 τηλ. : 26710-27311 fax : 26710-27312

Διαβάστε περισσότερα

ΙΑΤΡΟΦΙΚΗ ΦΡΟΝΤΙ Α ΓΙΑ ΤΑΞΙ ΙΩΤΕΣ ΣΥΝΤΟΜΗΣ ΚΑΙ ΜΑΚΡΑΣ ΙΑΡΚΕΙΑΣ

ΙΑΤΡΟΦΙΚΗ ΦΡΟΝΤΙ Α ΓΙΑ ΤΑΞΙ ΙΩΤΕΣ ΣΥΝΤΟΜΗΣ ΚΑΙ ΜΑΚΡΑΣ ΙΑΡΚΕΙΑΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΜΗΜΑ ΙΑΤΡΟΦΗΣ ΚΑΙ ΙΑΙΤΟΛΟΓΙΑΣ, ΤΕΙ ΚΡΗΤΗΣ ΙΑΤΡΟΦΙΚΗ ΦΡΟΝΤΙ Α ΓΙΑ ΤΑΞΙ ΙΩΤΕΣ ΣΥΝΤΟΜΗΣ ΚΑΙ ΜΑΚΡΑΣ ΙΑΡΚΕΙΑΣ ΕΠΙΜΕΛΕΙΑ: ΑΛΕΞΙΑ ΤΣΕΡΛΙΓΚΑ ΥΠΕΥΘΥΝΟΣ ΚΑΘΗΓΗΤΗΣ: Γ. Α. ΦΡΑΓΚΙΑ ΑΚΗΣ. 2012 σελ.

Διαβάστε περισσότερα

[1] P Q. Fig. 3.1

[1] P Q. Fig. 3.1 1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One

Διαβάστε περισσότερα

CHAPTER 101 FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD

CHAPTER 101 FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD CHAPTER FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD EXERCISE 36 Page 66. Determine the Fourier series for the periodic function: f(x), when x +, when x which is periodic outside this rge of period.

Διαβάστε περισσότερα

Concrete Mathematics Exercises from 30 September 2016

Concrete Mathematics Exercises from 30 September 2016 Concrete Mathematics Exercises from 30 September 2016 Silvio Capobianco Exercise 1.7 Let H(n) = J(n + 1) J(n). Equation (1.8) tells us that H(2n) = 2, and H(2n+1) = J(2n+2) J(2n+1) = (2J(n+1) 1) (2J(n)+1)

Διαβάστε περισσότερα

The Simply Typed Lambda Calculus

The Simply Typed Lambda Calculus Type Inference Instead of writing type annotations, can we use an algorithm to infer what the type annotations should be? That depends on the type system. For simple type systems the answer is yes, and

Διαβάστε περισσότερα

Uniform Convergence of Fourier Series Michael Taylor

Uniform Convergence of Fourier Series Michael Taylor Uniform Convergence of Fourier Series Michael Taylor Given f L 1 T 1 ), we consider the partial sums of the Fourier series of f: N 1) S N fθ) = ˆfk)e ikθ. k= N A calculation gives the Dirichlet formula

Διαβάστε περισσότερα

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ Γηπισκαηηθή Δξγαζία ηνπ Φνηηεηή ηνπ ηκήκαηνο Ζιεθηξνιόγσλ Μεραληθώλ θαη Σερλνινγίαο Ζιεθηξνληθώλ

Διαβάστε περισσότερα

Math221: HW# 1 solutions

Math221: HW# 1 solutions Math: HW# solutions Andy Royston October, 5 7.5.7, 3 rd Ed. We have a n = b n = a = fxdx = xdx =, x cos nxdx = x sin nx n sin nxdx n = cos nx n = n n, x sin nxdx = x cos nx n + cos nxdx n cos n = + sin

Διαβάστε περισσότερα

Notes are available 1

Notes are available 1 Notes are available 1 Galatians 2:15 4.12 2 3:15, 3:19 interpretational contradiction LAW cannot be and was added Promise 3 Gal.3:19 4 Mt 6:27 Which of you by taking thought can add one cubit unto

Διαβάστε περισσότερα

Advanced Subsidiary Unit 1: Understanding and Written Response

Advanced Subsidiary Unit 1: Understanding and Written Response Write your name here Surname Other names Edexcel GE entre Number andidate Number Greek dvanced Subsidiary Unit 1: Understanding and Written Response Thursday 16 May 2013 Morning Time: 2 hours 45 minutes

Διαβάστε περισσότερα

Living and Nonliving Created by: Maria Okraska

Living and Nonliving Created by: Maria Okraska Living and Nonliving Created by: Maria Okraska http://enchantingclassroom.blogspot.com Living Living things grow, change, and reproduce. They need air, water, food, and a place to live in order to survive.

Διαβάστε περισσότερα

On a four-dimensional hyperbolic manifold with finite volume

On a four-dimensional hyperbolic manifold with finite volume BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Numbers 2(72) 3(73), 2013, Pages 80 89 ISSN 1024 7696 On a four-dimensional hyperbolic manifold with finite volume I.S.Gutsul Abstract. In

Διαβάστε περισσότερα

Modern Greek Extension

Modern Greek Extension Centre Number 2017 HIGHER SCHOOL CERTIFICATE EXAMINATION Student Number Modern Greek Extension Written Examination General Instructions Reading time 10 minutes Working time 1 hour and 50 minutes Write

Διαβάστε περισσότερα

Instruction Execution Times

Instruction Execution Times 1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables

Διαβάστε περισσότερα

Solutions to Exercise Sheet 5

Solutions to Exercise Sheet 5 Solutions to Eercise Sheet 5 jacques@ucsd.edu. Let X and Y be random variables with joint pdf f(, y) = 3y( + y) where and y. Determine each of the following probabilities. Solutions. a. P (X ). b. P (X

Διαβάστε περισσότερα

ST5224: Advanced Statistical Theory II

ST5224: Advanced Statistical Theory II ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known

Διαβάστε περισσότερα

Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit

Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ting Zhang Stanford May 11, 2001 Stanford, 5/11/2001 1 Outline Ordinal Classification Ordinal Addition Ordinal Multiplication Ordinal

Διαβάστε περισσότερα

Matrices and Determinants

Matrices and Determinants Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z

Διαβάστε περισσότερα

(C) 2010 Pearson Education, Inc. All rights reserved.

(C) 2010 Pearson Education, Inc. All rights reserved. Connectionless transmission with datagrams. Connection-oriented transmission is like the telephone system You dial and are given a connection to the telephone of fthe person with whom you wish to communicate.

Διαβάστε περισσότερα

Παρελθόν. (Past) Formation. past imperfective. past perfective. active forms Α / Β Α Β

Παρελθόν. (Past) Formation. past imperfective. past perfective. active forms Α / Β Α Β 12 Παρελθόν (Past) In Greek there are three different sets of forms (both active and medio-passive), which refer to the past: the past perfective (αόριστος), the past imperfective (παρατατικός) and the

Διαβάστε περισσότερα

1 John 5. LGNT - September 6, 2019 Page 1. Book Chapter Verse. Word # 1 John Greek. # of words. Numeric value. Interlinear English.

1 John 5. LGNT - September 6, 2019 Page 1. Book Chapter Verse. Word # 1 John Greek. # of words. Numeric value. Interlinear English. Book Chapter Verse Interlinear English Word # 1 John Greek # of letters # of words Numeric value 230501 everyone 01709 ΠΑΣ 3 281 230501 01710 Ο 1 70 230501 believing 01711 ΠΙΣΤΕΥΩΝ 8 1845 230501 that 01712

Διαβάστε περισσότερα

ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΛΛΗΝΙΔΕΣ

ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΛΛΗΝΙΔΕΣ ΕΛΛΗΝΙΔΕΣ ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΚΔΟΣΗ ΤΗΣ ΣΟΡΟΠΤΙΜΙΣΤΙΚΗΣ ΕΝΩΣΗΣ ΕΛΛΑΔΟΣ - ΤΕΥΧΟΣ Νο 110 - Δ ΤΡΙΜΗΝΟ 2014 Το πρώτο βραβείο κέρδισε η Ελλάδα για την φωτογραφία Blue + Yellow = Green στον διαγωνισμό 2014 του

Διαβάστε περισσότερα

LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV. 4 February 2014

LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV. 4 February 2014 LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV 4 February 2014 Somewhere κάπου (kapoo) Nowhere πουθενά (poothena) Elsewhere αλλού (aloo) Drawer το συρτάρι (sirtari) Page η σελίδα (selida) News τα νέα (nea)

Διαβάστε περισσότερα

Fourier Series. MATH 211, Calculus II. J. Robert Buchanan. Spring Department of Mathematics

Fourier Series. MATH 211, Calculus II. J. Robert Buchanan. Spring Department of Mathematics Fourier Series MATH 211, Calculus II J. Robert Buchanan Department of Mathematics Spring 2018 Introduction Not all functions can be represented by Taylor series. f (k) (c) A Taylor series f (x) = (x c)

Διαβάστε περισσότερα

1 JOHN 4:1--5:12 The New Testament Eyewitnesses The Son

1 JOHN 4:1--5:12 The New Testament Eyewitnesses The Son 70 The Spirit Agreement that Jesus is the Son is the Revelation of the Spirit Apostles which is the Apostolic witness Children Thus those who believe the Apostles are children Witnesses to The Love of

Διαβάστε περισσότερα

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8  questions or comments to Dan Fetter 1 Eon : Fall 8 Suggested Solutions to Problem Set 8 Email questions or omments to Dan Fetter Problem. Let X be a salar with density f(x, θ) (θx + θ) [ x ] with θ. (a) Find the most powerful level α test

Διαβάστε περισσότερα

Second Order Partial Differential Equations

Second Order Partial Differential Equations Chapter 7 Second Order Partial Differential Equations 7.1 Introduction A second order linear PDE in two independent variables (x, y Ω can be written as A(x, y u x + B(x, y u xy + C(x, y u u u + D(x, y

Διαβάστε περισσότερα

Η ΔΙΑΣΤΡΕΥΛΩΣΗ ΤΗΣ ΕΛΛΗΝΙΚΗΣ ΓΛΩΣΣΑΣ ΜΕΣΩ ΤΩΝ SOCIAL MEDIA ΤΗΝ ΤΕΛΕΥΤΑΙΑ ΠΕΝΤΑΕΤΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΗΣ ΑΝΑΣΤΑΣΙΑΣ-ΜΑΡΙΝΑΣ ΔΑΦΝΗ

Η ΔΙΑΣΤΡΕΥΛΩΣΗ ΤΗΣ ΕΛΛΗΝΙΚΗΣ ΓΛΩΣΣΑΣ ΜΕΣΩ ΤΩΝ SOCIAL MEDIA ΤΗΝ ΤΕΛΕΥΤΑΙΑ ΠΕΝΤΑΕΤΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΗΣ ΑΝΑΣΤΑΣΙΑΣ-ΜΑΡΙΝΑΣ ΔΑΦΝΗ Η ΔΙΑΣΤΡΕΥΛΩΣΗ ΤΗΣ ΕΛΛΗΝΙΚΗΣ ΓΛΩΣΣΑΣ ΜΕΣΩ ΤΩΝ SOCIAL MEDIA ΤΗΝ ΤΕΛΕΥΤΑΙΑ ΠΕΝΤΑΕΤΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΗΣ ΑΝΑΣΤΑΣΙΑΣ-ΜΑΡΙΝΑΣ ΔΑΦΝΗ Τμήμα Δημοσίων Σχέσεων & Επικοινωνίας Τεχνολογικό Εκπαιδευτικό Ίδρυμα Ιονίων

Διαβάστε περισσότερα

FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17

FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17 FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17 Name: Surname: Date: Class: 1. Write these words in the correct order. /Γράψε αυτέσ τισ λέξεισ ςτη ςωςτή ςειρά. 1) playing / his / not /

Διαβάστε περισσότερα

Section 9.2 Polar Equations and Graphs

Section 9.2 Polar Equations and Graphs 180 Section 9. Polar Equations and Graphs In this section, we will be graphing polar equations on a polar grid. In the first few examples, we will write the polar equation in rectangular form to help identify

Διαβάστε περισσότερα

Τ.Ε.Ι. ΔΥΤΙΚΗΣ ΜΑΚΕΔΟΝΙΑΣ ΠΑΡΑΡΤΗΜΑ ΚΑΣΤΟΡΙΑΣ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ

Τ.Ε.Ι. ΔΥΤΙΚΗΣ ΜΑΚΕΔΟΝΙΑΣ ΠΑΡΑΡΤΗΜΑ ΚΑΣΤΟΡΙΑΣ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ Τ.Ε.Ι. ΔΥΤΙΚΗΣ ΜΑΚΕΔΟΝΙΑΣ ΠΑΡΑΡΤΗΜΑ ΚΑΣΤΟΡΙΑΣ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ Η προβολή επιστημονικών θεμάτων από τα ελληνικά ΜΜΕ : Η κάλυψή τους στον ελληνικό ημερήσιο τύπο Σαραλιώτου

Διαβάστε περισσότερα