Computer Science Ability Test aims to evaluate objectively, through unified examinations with 10 true or false questions, the abilities of testees in computer science. Kotori is taking the test, but soon she discovers with dismay that she cannot answer even a single question. Now she presents you with these 10 questions. Can you tell her the correct answer to each question?
Computer Science Ability Test (CSAT) aims to evaluate objectively, through unified examinations with 10 true or false questions, the abilities of testees in computer science. Kotori is taking the test, but soon she discovers with dismay that she cannot answer even a single question. Now she presents you with these 10 questions. Can you tell her the correct answer to each question? (On linear algebra) Two vectors v1v_1v1 and v2v_2v2 are linearly dependent if there exists two scalars k1k_1k1 and k2k_2k2 such that k1v1+k2v2=0→k_1v_1 + k_2v_2 = overrightarrow{0}k1v1+k2v2=0. (On calculus) ydx−xdyx2−y2=d(12ln∣x−yx+y∣)frac{ytext{d}x - xtext{d}y}{x^2-y^2} = text{d}(frac{1}{2}ln left| frac{x-y}{x+y} right|)x2−y2ydx−xdy=d(21ln∣∣∣x+yx−y∣∣∣). (On discrete mathematics) ∅⊆{∅}emptyset subseteq {emptyset}∅⊆{∅}. (On physics) One mole of ideal gas is expanded from V0V_0V0 to 2V02V_02V0 in a reversible adiabatic process. If the temperature of the gas decreases by 25%, the gas may be a type of monatomic gas. (On data structure) The amortized time complexity of an insert operation of a Fibonacci heap is O(1)O(1)O(1). (On approximation algorithm) If P≠NPP ne NPP=NP, there does not exist a polynomial-time 2-approximation algorithm for the traveling salesman problem on a complete graph, but there exists a polynomial-time 2n2^n2n-approximation algorithm for this problem. (On quantum algorithm) There exists a comparison-based quantum sorting algorithm which takes less than Ω(nlogn)Omega(nlog n)Ω(nlogn) steps and is better than classical algorithms. (On operating system) A system consists of 4 resources with the same type. Suppose that at most 3 processes simultaneously apply the resource and every process applies at most 2 resources, so the system is deadlock free. (On theory of computation) Let L(M)L(M)L(M) be the language that the Turing machine MMM accepts, then the language {"M"∣M is a Turing machine and L(M) is uncountable}{text{"}Mtext{"} | M text{ is a Turing machine and } L(M) text{ is uncountable} }{"M"∣M is a Turing machine and L(M) is uncountable} is recursively enumerable but not recursive. (On compiler principles) There exists a grammar which is LL(1) but not LALR(1).
