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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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6我國憲法第17條明定,人民有選舉、罷免、創制及複決之權。依司法院大法官解釋之意旨,下列敘述何 者錯誤? (A)民意代表候選人之參選學歷限制仍有其必要,為立法者設定之合理條件 (B)政黨推薦之候選人得減半繳納保證金之規定,無助於政黨政治之健全發展,違反平等原則 (C)在校肄業之學生依法不得登記為候選人,已對人民參政權形成過度限制,違反比例原則 (D)無政黨推薦之總統、副總統選舉候選人須繳納連署保證金,是為避免耗費社會資源,並無違反平等原則

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9. The   astute   diplomat navigated the tense negotiations, securing a favorable agreement for her country. (A) apathetic (B) astounding (C) oblivious (D) shrewd (E) sluggish

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26 依據消防法第 4 條規定,下列何者不屬於救火個人基本裝備?(A)消防衣、帽、鞋 (B)個人救命器 (C)胸燈 (D)熱顯像儀