18. Find the maximum = __⑱__ of f(x, y, z) = xyz subject to constraints x + y + z = 32, x - y + z = 0, x ≥ 0, y ≥ 0, and z ≥ 0.

19. Evaluatexy dy dx =__⑲__

20. Find the volume __⑳__ of the solid is bounded by r² + z² = a² and r = a cos θ.

1. 語句修繕 (5%): 請將以下機器翻譯出來的語句，改寫成語法正確、表達通順的中文。       「我最近了解到這個詞叫做『躺平』(quiet quitting)，意思是你不是徹底辭職，而是放棄超越自我的想法，」擁有超過 10,000 名粉絲的 TikTok 用戶 Zaiad Khan 在一次採訪中說，舒緩的聲音，與紐約市地鐵的視頻並列。「你仍在履行你的職責，但你不再在精神上認同工作必須是我們生活的那種忙碌文化。」

2. 換句話說 (5%):依照前一題對於「躺平」的定義，請您寫出五個「躺平」的同義詞，並依照語域高低，由高至低排列。

3. 翻譯評論 (10%): 以下英文段落出自十九世紀英國作家勃朗特 (Charlotte Brontë, 1816-1855) 長篇小說《簡愛》(Jane Eyre, 1847) 第八章，中文翻譯則分別出自一九三五年的伍光建譯本和一九三六年的李霽野譯本，請您仔細比較過後評論這兩個譯本的特色，並說明您偏好伍光建或李霽野的翻譯。 That night, on going to bed, I forgot to prepare in imagination the Barmecide supper of hot roast potatoes, or white bread and new milk, with which I was wont to amuse my inward cravings: I feasted instead on the spectacle of ideal drawings. (Brontë, 1847) 我向來最喜歡吃烤薯, 白麵包, 新鮮牛奶, 上床時總想到這幾件好吃的東西, 現在卻不然了； 我臨睡的時候, 所想的都是繪畫。(伍光建, 1935) 那一晚上床睡覺的時候, 平常我愛拿來滿足我內心渴望的那種畫餅充飢的烤馬鈴薯或白麵包和新鮮牛奶的晚餐, 我忘記在想像中預備了, 我卻拿我暗中見到的空幻的畫景來做盛宴。(李霽野, 1936)

II. English Ability 1. Paraphrasing: Rewrite the following paragraph in English to express the same meaning or information with different wording and structure.  An Immense World by Ed Yong is a book filled with strange creatures and experiments； Yong is interested in what animals perceive and what they might communicate to us. Humans see the world one way, and other species see it through very different eyes, and many don't see it at all. Attempting to exchange one worldview-or, to use the term Yong favors, Umwelt--for another may be frustrating, but, he argues, that's what makes the effort worthwhile. It reminds us that, "for all our vaunted intelligence," our Umwelt is just one among millions. Some species of scallops, for instance, have dozens of eyes； others have hundreds. We can learn a lot from the methods that animals use to sense their surroundings. And doing so can be, for us, mind-expanding.

2. Summarizing: Write a summary in English between 50 to 80 words to get the gist of the following paragraphs. (It is strongly recommended not to copy the same sentences of the original texts.)  Of the character sketches that the English satirist Samuel Butler wrote in the mid-seventeenth century- among them "A Degenerate Noble," "A Huffing Courtier," "A Small Poet," and "A Romance Writer"-the most recognizable today is "A Modern Critic." He is a contemptible creature: a tyrant, a pedant, a crackpot, and a snob； "a very ungentle Reader"； "a Corrector of the Press gratis"； "a Committee-Man in the Commonwealth of letters"； "a Mountebank, that is always quacking of the infirm and diseased Parts of Books." He judges, and, if authors are to be believed, he judges poorly. He praises without discernment. He invents faults when he cannot find any. Beholden to no authority, obeying nothing but the mysterious stirrings of his heart and his mind, he hands out dunce caps and placards insolently and with more than a little glee. Authors may complain to their friends, but they have no recourse. The critic's word is law. Butler's sketch would still strike a chord with aggrieved writers today, but, in his time, the Modern Critic- part mountebank, part magician was a new phenomenon. The figure's shape-shifting in the centuries since is the subject of John Guillory's new book, "Professing Criticism" (Chicago), an erudite and occasionally biting series of essays on "the organization of literary study." Guillory has spent much of his career explaining how works of literature are enjoyed, assessed, interpreted, and taught； he is best known for his landmark work, "Cultural Capital" (1993), which showed how literary evaluation draws authority from the institutions principally universities within which it is practiced. To suggest, for instance, that minor poets were superior to major ones, as T. S. Eliot did, or that the best modernist poetry was inferior to the best modernist prose, as Harold Bloom did, meant little unless these judgments could be made to stick-that is, unless there were mechanisms for transmitting these judgments to other readers.

III. Translation Competence  1. 英譯中: 請將下列英文翻譯成正確通順、適體適境的中文。Microsoft's $10bn bet on ChatGPT developer marks new era of AI  The $10bn investment that Microsoft is considering in San Francisco-based research outfit OpenAI looks set to become the defining deal for a new era of artificial intelligence. If the US software giant is right about the far-reaching implications of the technology, it could also trigger a realignment in the AI world as other tech groups race to stake out their place in the new field of generative AI.  OpenAI grabbed global headlines last month with the launch of ChatGPT, an AI system that can answer queries and produce text in natural-sounding language. But Microsoft executives believe the technology behind the service will soon have a deeper impact throughout the tech world. (Financial Times)

2. Chinese-to-English Translation : Translate the following Chinese text into correct, fluent and adequate English.  臺灣地處印太區域樞紐，以貿易立國，利用地理位置優勢創造國家利基，已為我國經濟發展打下穩固基礎。然而，全球化與第四次工業革命、貿易戰與 Covid-19 疫情所引發的供應鏈重組，以及數位經濟高速發展，所帶來的全球經濟發展模式改變，已經是現在進行式，更是未來可見的趨勢。為此，各國政府與產業，莫不積極在現今變動的浪潮中，超前部署，並且爭取優秀人才；而各國人才則努力在這變動中強化自己的競爭力，以期在激烈競爭中脫穎而出。(出自《2030 雙語政策整體推動方案》)

1. Clearing the Air        Getting to zero carbon emissions won't save the world. We will need to remove carbon on a massive scale. To do that will require a planet-wide effort to match anything that humankind has ever achieved. Scientists and entrepreneurs are embarking on ambitious projects to remove carbon dioxide from ambient air and lock it away. In Arizona, an engineering professor shows me his "mechanical tree," a single one of which he says may someday be able to do the work of a thousand regular trees in capturing and storing CO2. In Australia, a leading oceanographer tells me that seaweed is salvation, if only we'd help it grow in giant aqua-gardens of kelp [海帶] and wakame [裙帶菜] that could harbor billions of tons of carbon dioxide.         What these efforts have in common is that they are geared in the long run to drag downward a number that climate experts agree holds the key to the health of the planet. That number is the atmospheric concentration of carbon dioxide, which for thousands of years had held stable at or a bit below 280 parts per million, until the industrial revolution kicked off in the middle of the 19th century. Today this critical number stands at some 420 parts per million—in other words, the percentage of CO2 in the atmosphere has risen roughly 50 percent since 1850. (National Geographic, Nov. 2023)

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