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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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2.根據美國職棒大聯盟(MLB)2023年的新守備佈陣規則,下列何者不在此規則限制? (A)內野紅土區二壘左右任一側,都至少同時要有2名守備球員(B)當投手球出手時, 內野守備球員需雙腳完全站在內野紅土區(C)投手出手時,外野手站位不得跨區移 防超過中線至另一側(D)違反守備佈陣規則判守備方1顆壞球。

4.下列關於「運動i臺灣」2.0計畫之預期效益,何者敘述錯誤? (A)培育國民體適能指導員輔助全國體育活動,傳遞正確運動知能(B)辦理體適能檢 測服務達60萬人次以上(C)強化運動資訊平台功能,服務人次達800萬人次以上 (D)整合與深化跨部會運動推展業務合作機制。

49. 將 164 g 甘油(C3H8O3)加入 338 mL 水溶液,請問該溶液在 39.8°C 下之蒸氣壓為何?已知純 水在 39.8°C 下之蒸氣壓為 54.74 torr,水的密度為 0.992 g/cm³。 (A) 35.37 torr (B) 49.96 torr (C) 57.12 torr (D) 63.89 torr

38. 依職業安全衛生設施規則規定,設置固定式圓盤鋸、帶鋸、手推刨床、截角機等合計在幾台以上時,應指定作業管理人員? (A)3 (B)5 (C)10 (D)30 。

27 依據消防法第 6 條規定,不屬於各類場所消防安全設備設置標準應設置火警自動警報設備之旅館、老人福利機構場所及中央主管機關公告場所之管理權人,應設置何種設備並維護之? (A)住宅用火災警報器 (B)自動撒水設備 (C)緩降機 (D)滅火器

50 災害防救法所稱公共事業,指經中央目的事業主管機關指定之事業,下列何者錯誤? (A)大眾傳播事業 (B)運輸業 (C)石油業 (D)液化石油氣業