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25. (4 points) Which of the following statements are correct? (A) If Q is orthogonal, then det(Q) = = +1. (B) Let A be a real n x n matrix. Then A is symmetric if and only if A is orthogonally equivalent to a real diagonal matrix. (C) Let A E Rixm be a matrix whose characteristic polynomial splits over R. Then A is orthogonally equivalent to a real upper triangular matrix. (D) Let T be a self-adjoint (Hermitian) operator on a finite-dimensional inner product space V. Then every eigenvalue of T is positive. (E) Let T be a self-adjoint (Hermitian) operator on a finite-dimensional inner product space V. Then every eigenvalue of T is negative.

24. (4 points) Let Wi and Wa be subspaces of a finite-dimensional vector space V. Let 6 denote the direct sum. Which of the following statements are correct? (A) Win Wa is a subspace of V. (B) WiUW2 is a subspace of V. (C) W1+W2 is a subspace of V. (D) If V = Wi @ Wa, and Bi and Be are bases for Wi and Wa, respectively, then Bi O Bz = 0, and B1 U Bz is a basis for V. (E) If Wi e Wa = V, then the dimension dim(V) = dim(Wi)+dim(Wz).

23. (4 points) Which of the following statements are NOT correct? (A) If S is linearly independent and generates V, each vector in V can be expressed uniquely as a linear combination of vectors in S. (B) Every vector space has at least two distinct subspaces. (C) No vector is its own additive inverse. (D) All vector spaces having a basis are fnitely generated. (E) Any two bases in a finite-dimensional vector space V have the same number of elements.

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12.有關Mycobacterium leprae的敘述,下列何者最不適當?(A)引起漢生病(Hansen's disease) (B)會損害周圍神經 (C)屬於快速生長mycobacteria (D)屬於抗酸桿菌

5. Consumers are _____ interested in having information on the provenance and quality of their food, and food safety remains a keen point of interest. (A) rarely (B) slightly (C) increasingly (D) reluctantly

6. Horses used for racing are usually housed in _____ and close confinement, which causes these social, plains-ranging animals, major distress. (A) freedom (B) isolation (C) companionship (D) excitement

17. 下列關於胰臟炎的描述,何者錯誤? (A) 高尿酸血症是導致慢性胰臟炎的最常見原因 (B) 高三酸甘油酯血症可能導致急性胰臟炎 (C) 脂肪酶(Lipase)指數上升是診斷急性胰臟炎的重要依據之ㄧ (D) 慢性胰臟炎可能導致糖尿病

48. NFC 支付通常有三個主要的組成元素,不包括下列何者? (A)手機的 NFC 天線 (B)手機內建防干擾的安全元件 (C)商店收銀台的非接觸式讀卡機 (D) RFID 無線射頻辨識

49.新加坡政府為打造成為「智慧國家」,積極推動金融保險科技的發展。而下列敘述何者錯誤? (A)成立國際智慧金融中心,提升金融科技發展效率 (B)成立金融科技辦公室,提供金融保險科技一站式支持 (C)建置金融保險科技平台,加強監理機關與科技業者間之交流 (D)設置金融創新網路(AFIN)實驗環境,降低金融科技實驗成本