113年清華大學（後西醫） — 資訊科學

共 40 題 · 含 AI 詳解

#1 A uniform disk of mass $m$ and radius $R$ (so the moment of inertia $I_{CM} = \frac{1}{2}mR^2$… › #2 Determine the height of the center of mass of a solid uniform pyramid that has f… › #3 Two speakers both produce sound wave of power = $400\pi$ Watt, frequency = $170$… › #4 Two thin lenses form a compound lens system. The front focal length ($FFL$) of t… › #5 Which of the following statements is correct? › #6 In the circuit, if the switch S is closed for a long time, and is then opened. J… › #7 What is the root-mean-square value of a triangular wave with its maximum voltage… › #8 A solid rod with length $L$, resistance $R$ and mass $M$ initially rotates with… › #9 Which quantity cannot be measured by Hall effect? › #10 A cord is wrapped on a pulley (treated as a uniform solid disk) of mass $M$ and… › #11 The average power transferring along the string can be written as $P = \mu v^a \omega^b A^c /2$… › #12 A shear force of $600\text{ N}$ is applied to one face of an alloy cube with sid… › #13 Consider two different diatomic ideal gases ($N_1$ and $N_2$) kept in two separa… › #14 There is an electric dipole in an external uniform $E$-field, as shown below. Ex… › #15 Referring to the DC circuit shown below with the capacitor C been fully charged,… › #16 Two short uniform cylindrical-shaped magnetic bars, with identical length $L$ an… › #17 The double-slit experiment also exhibits diffraction effects, as the slits have… › #18 A particle of mass 1 kg is confined to move in the one-dimensional region $x > 0$… › #19 Consider a uniform metal bar with both ends in contact with thermal reservoirs,… › #20 Beat is an interference phenomenon when two waves of slightly different frequenc… › #21 John skates on the ground subject to a friction force. For a stationary observer… › #22 For a 2D monatomic ideal gas, which of the following statements is true? › #23 For two inductors connected in parallel, see the figure below; which of the foll… › #24 For a classical electromagnetic plane wave travelling in a vacuum, which of the… › #25 Which statement correctly describes the Bohr model of the hydrogen atom? › #26 Suppose $A$ is a $4 \times 4$ real matrix and $v_1, v_2, v_3, v_4$ are four line… › #27 Suppose $A$ is a $2 \times 3$ real matrix and $B$ is a $3 \times 2$ real matrix.… › #28 Suppose $A = \begin{bmatrix} 3 & 2 \ 2 & 3 \ 2 & -2 \end{bmatrix}$ and… › #29 Suppose $A = \begin{bmatrix} 1 & -1 & 2 \ 1 & 1 & 0 \end{bmatrix}$ and… › #30 Suppose $A$ is a $3 \times 3$ invertible matrix and $I_3$ is the $3 \times 3$ id… › #31 If $\|\mathbf{u}\|=8$ and $\|\mathbf{v}\|=3$, then what are the largest possible… › #32 Consider the system of linear equations: $ x + 7y - 6z = 6 $ $ 2x + 11y - 8z = 7 $… › #33 Given the row-reduced echelon form… › #34 Let $A = \begin{bmatrix} 1 & -4 & 4 \ 0 & 1 & -1 \ 1 & -2 & 1 \end{bmatrix}$, wh… › #35 An $n \times n$ skew-symmetric matrix $A$ is defined as $A^t = -A$. Please find… › #36 A vector space is spanned by $\{1, \cos(t), \sin(t)\}$ for $-\pi \le t \le \pi$.… › #37 A quadratic equation is described as: $x^2 + 8xy + 7y^2 = 225$. Which of the fol… › #38 Which of the following statements is true? › #39 Consider the matrix $A = \begin{pmatrix} 3 & 2 \ 2 & 6 \end{pmatrix}$. How many… › #40 Consider the Fibonacci series $a_0 = 1$, $a_1 = 2$, and $a_n = a_{n-1} + a_{n-2}$… ›