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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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14. 依教育部《幼兒園教保活動課程大綱》,有關「美感」領域學習指標「 美-中-3-1-2 樂於參與在地藝術創作或展演活動」,下列說明何者正確? (A)「表現與創作」能力;「情意」學習面向 (B)「表現與創作」能力;「藝術媒介」學習面向 (C)「回應與賞析」能力;「情意」學習面向 (D)「回應與賞析」能力;「藝術媒介」學習面向

64.美國學校心理健康(school mental health)採用多層級(multitiered)模式,社會與情緒學習(social and emotional learning, SEL)及正向行為介入與支持(positive behavioral interventions and supports, PBIS)等方式 適合職能治療師於下列何種層級使用? (A)全校層級(層級一) (B)目標介入層級(層級二) (C)強化介入層級(層級三) (D)特殊介入層級(層級四)

66.有關民國 106 年 12 月 6 日新修訂之《偏遠地區學校教育發展條例》,下列說明何者正確? (A)村、里或部落內有國民小學學齡兒童十七人以上,然未設學校者,應設立國民小學分校或分班 (B)最近公立國民小學距離村、里或部落辦公處所五公里以上,且無大眾運輸或免費交通工具可到達者,應設立國民小學分校或分班 (C)專聘教師連續任滿五年,且依前項取得第二專長,表現優良者, 得一次再聘五年或依其意願參加專任教師甄選,並予以加分優待 (D)偏遠地區國民小學全校學生人數未滿三十人且採混齡編班者,除置校長及必要之行政人力外,其教師員額編制,得以生師比五比一 計算但教師員額最低不得少於三人

16 下列那一種政府預算制度特別重視決策案的優先順序排列?(A)行政預算 (B)計畫預算 (C)零基預算 (D)項目預算

29. (A) since (B) while (C) unless (D) provided

1 Esping-Andersen 區分三種西方福利國家體制所運用的指標,下列何者正確? (A)去商品化、階層化 (B)去商品化、性別主流化 (C)市場化、階層化 (D)福利私有化、階層化