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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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48 「今夜鄜州月,閨中只獨看;遙憐小兒女,未解憶長安。香霧雲鬟濕,清輝玉臂寒;何時倚虛幌?雙照淚痕乾。」下列何者所抒發的情感與此詩最相近? (A)美人捲珠簾,深坐顰蛾眉;但見淚痕濕,不知心恨誰 (B)寥落古行宮,宮花寂寞紅;白頭宮女在,閒坐說玄宗 (C)君問歸期未有期,巴山夜雨漲秋池;何當共剪西窗燭,卻話巴山夜雨時 (D)紗窗日落漸黃昏,金屋無人見淚痕;寂寞空庭春欲晚,梨花滿地不開門

49 「我時常看見你穿著白衣/在往診的道路上顛簸/專注構思社會診斷書/在寂寞的夜晚/熬成一篇一篇 新文學的先聲/歲末天寒迎接年節/家家戶戶焚燒紙錢賄賂鬼神/你卻在自家庭院/默默點燃/貧苦病 患無力償還的帳單。」下列何者最適合描述本詩所歌詠的人物形象? (A)涓滴歸公 (B)宵衣旰食 (C)恫瘝在抱 (D)披星戴月

12 有關 Benzodiazepine(BZD)的護理指導,下列何者最適當? (A) BZD 是代謝較快的藥物,將可以改善其記憶力 (B) BZD 類藥物主要就是鎮靜安眠,無法用來抗焦慮 (C)建議勿飲酒的主要原因是酒精促排尿,就會大量將 BZD 排出 (D)長期服用 BZD 可能造成依賴,戒斷時宜逐漸減量

54. 下列哪一個情境設定最適合做為除法的啟蒙問題?(A) 離散量等分除情境 (B) 離散量包含除情境(C) 連續量等分除情境 (D) 連續量包含除情境

54. 下列哪一個情境設定最適合做為除法的啟蒙問題?(A) 離散量等分除情境 (B) 離散量包含除情境(C) 連續量等分除情境 (D) 連續量包含除情境

55. 有一個數學問題:「公升的果汁,相當於裝成瓶,沒有裝滿的那一瓶是多少公升?」下面哪一個算式能算出正確的答案? (A) (B) (C) (D)