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50. An electric diple consists of point charges ±? a distance 2a apart. The potential at an arbitrary point P can be expressed as V(P) = k? r+ + k(−?) r− = k?(r−−r+) r+r− , where k is the Coulomb constant, r+ is the distance to the point charge +?, r− is the distance to the point charge −?. If r is the distance to the dipole center, for r ≫ a, the quantities r+, r−, and r are nearly the same as r2 ≈ r+r−. The difference between the distances from the two charges to P, that is, r− − r+, is approximately equal to 2a cos ?, where ? is the angle as shown in the figure. Eventually, the dipole potential for r ≫ a becomes V(r, ?) = k(2a?) cos ? r2 . What is the electric field ?⃗⃗ at an arbitrary position P for r ≫ a? Note that îand ?̂are unit vectors. (A) ?⃗⃗ = k(2a?) r3 [(3 cos2 ? − 1)î+ sin ? cos ? ?̂] (B) ?⃗⃗ = k(2a?) r3 [(3 sin2 ? − 1)î+ 3 sin ? cos ? ?̂] (C) ?⃗⃗ = k(2a?) r [(3 cos2 ? − 1)î+ 3 sin ? cos ? ?̂] (D) ?⃗⃗ = k(2a?) r2 [(3 cos2 ? − 1)î+ 3 sin ? cos ? ?̂] (E) ?⃗⃗ = k(2a?) r3 [(3 cos2 ? − 1)î+ 3 sin ? cos ? ?̂]

49. Consider a soap bubble and a liquid drop of the same radius. If both have the same surface tension γ, radius R, and external pressure P0, what is the relationship between the internal pressure of the soap bubble (Pbubble) and the internal pressure of the liquid drop (Pdrop)? (A) Pbubble > Pdrop (B) Pbubble < Pdrop (C) Pbubble = Pdrop (D) Cannot be compared

48. A bullet of mass m is fired horizontally with a speed v into a stationary wooden block of mass M and becomes embedded in it. If the block is suspended by a string of length L (forming a simple pendulum system), what fraction of the initial kinetic energy is lost as mechanical energy during the moment of impact? (A) m / (m + M) (B) M / (m + M) (C) m / M (D) (M - m) / (M + m)

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四、問答(20 分) 1.請你以本土語言教師的專業,寫出一份訓練高中生參加臺中市賽複賽當中的「臺灣台語情境式演說」的培訓計畫,訓練期間是以三個月為準,比賽規則是按照 115 年全國語文競賽的臺灣台語情境式演說實施要點 為準。

(二)請你共以下的臺羅翻譯做漢字。 Tsit ê sî-tsūn, bô-tiunn-tî, tshiū-thâu-tíng tshenn-tî-á ê kiò-siann kā khùn--khì ê sè-kài kiò tsing-sîn, suà--lâi, tang-sì thiah-ha̍h, ji̍t-thâu mā ta̍uh-ta̍uh-á thàu tshut kng, tsiò tī muá-suann-phiânn ê tsháu-á kah hue-luí. Tang-pîng ê suann-thâu ná lâi ná kng, kā tshīng kui ê kuânn-thinn ê kāu-sann thǹg-tiāu, àm-tām ê sim-tsîng mā-sī. 「Tsiânn hó, guá tsáu tsit tsuā tsin-tsiànn ū kè-ta̍t, suann-tíng tō-sī siōng kín pha̍ktio̍h ji̍t-thâu ê sóo-tsāi, koh ū iām-lē ê kíng-sik sio-puê-tuè.Kā ba̍k-tsiu hiòng hn̄g ê sóo-tsāi khuànn, suann-kha ê tuā-káng, ji̍t-tshiu tshiō tī tsi̍t lîng iū tsi̍t lîng ê tsuí-iann, tán-bē-hù ê tsûn-tsiah, tō beh lâi khí-phâng.

三、短文對譯:以下是對凃至彧〈一月——寫予佇台語路懸頂的家己〉這篇文章改寫的。請你翻譯下面這篇文章。(20 分)(一)請你共以下的漢字翻譯做臺羅。寒凊的天氣籠罩土地,四界的動物猶原咧睏,塗裡的種子嘛猶未暴穎。逐工覕佇厝內,想欲欣賞無仝景緻的我,疊像棉襀被彼款的衫出門。「四序溫暖的天氣欲去佗位揣?應該是去上倚日頭的山頂。」予天氣冷甲槌槌----我是按呢想。著急欲曝著日頭,一點仔攏無躊躇就上山矣。寒冷的東北風拍蹛我的身軀,山煞愈懸愈冷,風是愈懸愈透。遐爾仔拚勢,四界走揣的我忝矣,倒佇咧倒去的樹身頂。寒凍的冷風貫入我的衫,揻入我的骨。我較睏嘛睏袂去,所致就坐佇石頭頂懸,看四箍圍仔的烏,看甲出神。

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2. 下列何者不是《幼兒園教保活動課程大綱》中「語文領域」的領域目標? (A)體驗與覺知語文的趣味與功能 (B)慣於敘說經驗與編織故事 (C)喜歡閱讀並展現社會觀點 (D)認識並欣賞社會中使用多種語文的情形

21. 教育部將民國 103 年定為「美感教育年」開始積極推動美感教育,落實學生對美的體驗與實踐。下列哪位學者最早提出「美育」(aesthetic education)的概念,主張「人唯有透過美感教育,才能使得人類的感性、理性與精神性動力,獲得整體和諧的開展,以造就完美人格, 進而促進和諧社會之建立。」? (A)康德(I. Kant) (B)席勒(Friedrich Schiller) (C)阿德勒(M. Adler) (D)馬勒席爾(M. Mothersill)

23. 張老師認為知識的形成,是個人將各種對於某個事物的不同見解加以統合。例如個人將關於某事物的科學觀點、特殊經驗,以及社會對該事物的信念等等,加以組合成為自己對該事物的知識,這便是對個人最有意義的知識。請問他這種知識觀點屬於下列何者? (A)觀念主義 (B)實用主義 (C)建構主義 (D)經驗主義

24. 小強老師帶著班級前往山上健行,路上遭遇蜂群攻擊,小強老師沒想那麼多就立刻掩護同學撤離並以自身吸引蜂群攻擊火力,而撤離至後方的同學則報警請求支援,最後小強老師經特搜隊及時救援而保住一命。這個情境彰顯了下列哪一項教育倫理學的重要理念? (A)達爾文主義(Darwinism) (B)義務倫理學(Deontology) (C)效益論倫理學(utilitarianism ethics) (D)利他主義(altruism)

61. 依據衛福部之《目睹家庭暴力兒童及少年輔導處遇原 則》,學校受理案件後應於幾日內回覆教育主管機關? (A)24 小時 (B)3 日 (C)7 日 (D)30 日

2. 企業持有以下何種證券並無一定的償還期限?(A)股票(B)公債(C)國庫券(D)公司債