114年清華大學（後西醫） — 進階物理與線性代數

共 40 題 · 含 AI 詳解

#1 A bead of mass $m$ is constrained to move on a massless circular hoop of radius… › #2 Two masses $m_1$ and $m_2$ placed on a flat surface are connected by a spring of… › #3 A pendulum is composed of a bob of mass $m_2$, a rigid string of length $\ell$ a… › #4 Jack is pushing a box moving at a constant speed on a horizontal ground. Due to… › #5 The membrane serves as an insulator that separates the environments inside and o… › #6 In the double-slit experiments of neutrons, which of the following statements is… › #7 An ideal LC circuit with inductor L and capacitor C is initially charged with ze… › #8 For an RL circuit used as a low-pass or high-pass filter, which of the following… › #9 A ball of mass $m$ is connected by a string of length $L$ to a pivot fixed in pl… › #10 Two uniform ladders, both of length $L$, are hinged at point $A$ and tied togeth… › #11 One mole of real gas with interaction between molecules obeys van der Waals equa… › #12 A heat engine using monatomic ideal gas undergoes a cyclic process $BACB$, where… › #13 A cylinder has insulating walls and is divided into two parts by a frictionless… › #14 A particle with mass $m$ and positive charge $q$ starts from rest at the origin… › #15 The Maxwell's equations related to static magnetic field are $\nabla \cdot \vec{B} = 0$… › #16 Consider the $n=4$ states of hydrogen, what is the minimum angle $\theta$ betwee… › #17 Two blocks (with the same mass $m$) connected by a spring of negligible mass are… › #18 A block of mass $M$ is attached to a spring of mass $m$ and force constant $K$.… › #19 Imagine that an ideal monatomic gas is taken from its initial state $B$ to state… › #20 To explain the phenomenon of condensation of real gases to liquids, two constant… › #21 A solenoid consisting of $n$ turns per unit length with length $4a$, equal to fo… › #22 When an $LRC$ series circuit is driven at resonance, which of the following stat… › #23 An antiproton has the same rest mass as a proton which is created in the reactio… › #24 For getting a reasonable sensitivity to differentiate the Compton wavelength shi… › #25 As measured in an order of magnitude, which quantity of the following objects is… › #26 What is the determinant of the following matrix?… › #27 Let $L(x) = Ax$ represent a linear transformation from $\mathbb{R}^2$ to $\mathbb{R}^2$… › #28 Consider the system of linear equations: $$\begin{matrix} x+y+az=b \ x-2y+z=1 \ x-8y-11z=-7 \end{matrix}$$… › #29 Let $\{v_1,v_2,v_3\} = \{[1,1,0]^T, [0,1,1]^T, [1,0,1]^T\}$ and… › #30 For the matrix $$M = \begin{pmatrix} 3 & 1 & -2 \ -1 & 0 & 5 \ -1 & -1 & 4 \end{pmatrix}$$… › #31 Consider $\{0\}$ and $\{1\}$ as the basis for a vector space in $\mathbb{C}^2$,… › #32 Let $\mathbb{R}^{4\times 4}$ denote the collection of all $4 \times 4$ real matr… › #33 Let $\mathbb{R}^6$ denote the 6-dimensional real vector space and $\|\cdot\|$ de… › #34 Let $R_\theta$ denote the rotation matrix through an angle $0 < \theta < \frac{\pi}{4}$… › #35 Given a matrix $$A = \begin{bmatrix} 1 & 2 \ 3 & 2 \end{bmatrix}.$$ Find the eig… › #36 What are the dimensions of the row space, column space, and null space for the m… › #37 A linear equation system $Ax=b$ consists of $m$ linear equations with $n$ variab… › #38 If a linear transformation $\mathbf{T}: \mathbb{R}^3\rightarrow \mathbb{R}^3$ is… › #39 Which of the following statements is true? › #40 Consider the continuous function $f(x) = 3\cos 2x + 4\sin 2x$, and let $g(x) = a\cos x + b\sin x$… ›