MikaStars39/nano-eval huggingface dataset:
The electric field amplitude of a uniform plane wave is $E_{\mathrm{i m}}=100 \ \ \mathrm{V / m}$, vertically incident from air onto the surface of a lossless medium (where the medium parameters are $\sigma_{2}=0$, $\varepsilon_{t2}=4$, $\mu_{r2}=1$). Find the electric field amplitudes of the reflected wave and the transmitted wave.

Options:
A. $$
= 6 8. 0 \mathrm{~ V / m}
$$
B. $$
= 5 9. 5 \mathrm{~ V / m}
$$
C. $$
= 8 8. 8 \mathrm{~ V / m}
$$
D. $$
= 6 4. 4 \mathrm{~ V / m}
$$
E. $$
= 6 6. 6 \mathrm{~ V / m}
$$
F. $$
= 7 7. 7 \mathrm{~ V / m}
$$
G. $$
= 5 3. 2 \mathrm{~ V / m}
$$
H. $$
= 7 0. 2 \mathrm{~ V / m}
$$
I. $$
= 7 5. 4 \mathrm{~ V / m}
$$
J. $$
= 6 0. 0 \mathrm{~ V / m}
$$
Answer: E
$z < 0$ represents free space, while the region where $z > 0$ is a conductive medium ($\varepsilon = 20 \; \mathrm{pF/m}$, $\mu = 5 \; \mathrm{\mu H/m}$, and $\sigma = 0.004 \; \mathrm{S/m}$). A uniform plane wave is incident perpendicularly on the interface, with the incident electric field given by $E_{\mathrm{ix}} = 100 \mathrm{e}^{-\alpha_{t} z} \times \operatorname{cos} \left( 10^{8} t - \beta_{t} z \right) \; \mathrm{V/m}$. Find the transmitted wave's electric field $E_{\mathrm{tx}}$.

Options:
A. $$
= 9 7. 8 e^{-0. 7 8 t} \operatorname{c o s} {( 1 0^{8} t-1. 2 7 z+1 6. 8^{\circ} )} \ \mathrm{V / m}
$$
B. $$
= 9 7. 6 e^{-0. 8 0 t} \operatorname{c o s} {( 1 0^{8} t-1. 2 6 z+1 7. 1^{\circ} )} \ \mathrm{V / m}
$$
C. $$
= 9 6. 8 e^{-0. 7 3 t} \operatorname{c o s} {( 1 0^{8} t-1. 3 0 z+1 7. 4^{\circ} )} \ \mathrm{V / m}
$$
D. $$
= 9 8. 2 e^{-0. 8 1 t} \operatorname{c o s} {( 1 0^{8} t-1. 2 9 z+1 9. 1^{\circ} )} \ \mathrm{V / m}
$$
E. $$
= 9 7. 3 e^{-0. 7 8 t} \operatorname{c o s} {( 1 0^{8} t-1. 2 4 z+1 6. 7^{\circ} )} \ \mathrm{V / m}
$$
F. $$
= 9 8. 1 e^{-0. 7 2 t} \operatorname{c o s} {( 1 0^{8} t-1. 2 0 z+1 6. 9^{\circ} )} \ \mathrm{V / m}
$$
G. $$
= 9 7. 9 e^{-0. 7 9 t} \operatorname{c o s} {( 1 0^{8} t-1. 2 8 z+1 6. 5^{\circ} )} \ \mathrm{V / m}
$$
H. $$
= 9 7. 5 e^{-0. 7 8 t} \operatorname{c o s} {( 1 0^{8} t-1. 2 5 z+1 5. 2^{\circ} )} \ \mathrm{V / m}
$$
I. $$
= 9 6. 4 e^{-0. 7 6 t} \operatorname{c o s} {( 1 0^{8} t-1. 3 1 z+1 8. 4^{\circ} )} \ \mathrm{V / m}
$$
J. $$
= 9 8. 0 e^{-0. 7 5 t} \operatorname{c o s} {( 1 0^{8} t-1. 2 3 z+1 6. 3^{\circ} )} \ \mathrm{V / m}
$$
Answer: A
A linearly polarized uniform plane wave is obliquely incident from free space onto the boundary of an ideal medium characterized by $\boldsymbol{\sigma}_{1}=0 \,, \, \boldsymbol{\sigma}_{t 1}=4 \,, \, \boldsymbol{\mu}_{t 1}=1$. If the angle between the electric field of the incident wave and the plane of incidence is 45°, find: What percentage of the incident wave's average power is reflected?

Options:
A. $$
= \ 1 2 \ \%
$$
B. $$
= \ 2 0 \ \%
$$
C. $$
= \ 1 0 \ \%
$$
D. $$
= \ 2 2 \ \%
$$
E. $$
= \ 1 8 \ \%
$$
F. $$
= \ 2 8 \ \%
$$
G. $$
= \ 3 5 \ \%
$$
H. $$
= \ 3 0 \ \%
$$
I. $$
= \ 1 5 \ \%
$$
J. $$
= \ 2 5 \ \%
$$
Answer: E
When designing a uniform transmission line, polyethylene $( \, \varepsilon_{r}=2. \, 2 5 \, )$ is used as the dielectric. Assuming no loss, for a parallel two-wire line with an impedance of 300 Ω, what should the spacing between the wires be if the radius of the conductor is 0.6 mm?

Options:
A. $$
= 2 3. 5 \ \mathrm{m m}
$$
B. $$
= 2 7. 5 \ \mathrm{m m}
$$
C. $$
= 2 3. 9 \ \mathrm{m m}
$$
D. $$
= 2 4. 3 \ \mathrm{m m}
$$
E. $$
= 2 6. 3 \ \mathrm{m m}
$$
F. $$
= 2 6. 8 \ \mathrm{m m}
$$
G. $$
= 2 4. 7 \ \mathrm{m m}
$$
H. $$
= 2 5. 5 \ \mathrm{m m}
$$
I. $$
= 2 7. 1 \ \mathrm{m m}
$$
J. $$
= 2 5. 0 \ \mathrm{m m}
$$
Answer: H
Let the wire bend into a ring shape. What is the radiation resistance of a wire whose source frequency is $f=1 \ \ \mathrm{MHz}$ and whose line length is not equal to 1m?

Options:
A. $$
= 3. 1 7 \times1 0^{-8} \Omega
$$
B. $$
= 3. 0 5 \times1 0^{-8} \Omega
$$
C. $$
= 1. 9 0 \times1 0^{-8} \Omega
$$
D. $$
= 2. 8 0 \times1 0^{-8} \Omega
$$
E. $$
= 2. 6 5 \times1 0^{-8} \Omega
$$
F. $$
= 2. 5 1 \times1 0^{-8} \Omega
$$
G. $$
= 2. 7 6 \times1 0^{-8} \Omega
$$
H. $$
= 1. 5 8 \times1 0^{-8} \Omega
$$
I. $$
= 2. 4 4 \times1 0^{-8} \Omega
$$
J. $$
= 2. 3 9 \times1 0^{-8} \Omega
$$
Answer: I
The reaction between bromoisobutane and sodium ethoxide in ethanol solution proceeds as follows:
$$
\mathrm{(A)~i-C_{4}H_{9}Br + (B)~C_{2}H_{5}ONa \longrightarrow (P)~NaBr + (S)~i-C_{4}H_{9}OC_{2}H_{5}}
$$
The initial concentrations of the reactants are known to be $c_{\mathrm{A0}} = 50.5 \, \mathrm{mol/m^3}$ and $c_{\mathrm{B0}} = 76.2 \, \mathrm{mol/m^3}$, and there are no products present in the raw materials. After reacting for a period of time at 95°C, analysis shows that $c_{\mathrm{B}} = 37.6 \, \mathrm{mol/m^3}$. Determine the concentrations of the remaining components at this point is ().

Options:
A. $$
c_{\mathrm{A}} \!=\! 1 2. 7 \, \, \, \mathrm{m o l / m^{3}}
$$
$$
c_{\mathrm{P}} \!=\! 3 7. 6 \, \mathrm{~ m o l / m}^{3}
$$
$$
c_{\mathrm{S}} \!=\! 3 5. \, \, \, 3 \, \, \, \mathrm{m o l / m}^{3}
$$
B. $$
c_{\mathrm{A}} \!=\! 1 4. 1 \, \, \, \mathrm{m o l / m^{3}}
$$
$$
c_{\mathrm{P}} \!=\! 3 6. 2 \, \mathrm{~ m o l / m}^{3}
$$
$$
c_{\mathrm{S}} \!=\! 3 8. \, \, \, 9 \, \, \, \mathrm{m o l / m}^{3}
$$
C. $$
c_{\mathrm{A}} \!=\! 1 4. 5 \, \, \, \mathrm{m o l / m^{3}}
$$
$$
c_{\mathrm{P}} \!=\! 3 5. 5 \, \mathrm{~ m o l / m}^{3}
$$
$$
c_{\mathrm{S}} \!=\! 4 0. \, \, \, 0 \, \, \, \mathrm{m o l / m}^{3}
$$
D. $$
c_{\mathrm{A}} \!=\! 1 2. 0 \, \, \, \mathrm{m o l / m^{3}}
$$
$$
c_{\mathrm{P}} \!=\! 3 9. 3 \, \mathrm{~ m o l / m}^{3}
$$
$$
c_{\mathrm{S}} \!=\! 3 6. \, \, \, 1 \, \, \, \mathrm{m o l / m}^{3}
$$
E. $$
c_{\mathrm{A}} \!=\! 1 1. 0 \, \, \, \mathrm{m o l / m^{3}}
$$
$$
c_{\mathrm{P}} \!=\! 3 4. 9 \, \mathrm{~ m o l / m}^{3}
$$
$$
c_{\mathrm{S}} \!=\! 3 2. \, \, \, 7 \, \, \, \mathrm{m o l / m}^{3}
$$
F. $$
c_{\mathrm{A}} \!=\! 1 1. 9 \, \, \, \mathrm{m o l / m^{3}}
$$
$$
c_{\mathrm{P}} \!=\! 3 8. \, 6 \, \mathrm{~ m o l / m}^{3}
$$
$$
c_{\mathrm{S}} \!=\! 3 8. \, \, 6 \, \, \, \mathrm{m o l / m}^{3}
$$
G. $$
c_{\mathrm{A}} \!=\! 1 3. 5 \, \, \, \mathrm{m o l / m^{3}}
$$
$$
c_{\mathrm{P}} \!=\! 4 0. 8 \, \mathrm{~ m o l / m}^{3}
$$
$$
c_{\mathrm{S}} \!=\! 3 6. \, \, \, 4 \, \, \, \mathrm{m o l / m}^{3}
$$
H. $$
c_{\mathrm{A}} \!=\! 1 3. 3 \, \, \, \mathrm{m o l / m^{3}}
$$
$$
c_{\mathrm{P}} \!=\! 3 8. 0 \, \mathrm{~ m o l / m}^{3}
$$
$$
c_{\mathrm{S}} \!=\! 3 7. \, \, \, 6 \, \, \, \mathrm{m o l / m}^{3}
$$
I. $$
c_{\mathrm{A}} \!=\! 1 3. 9 \, \, \, \mathrm{m o l / m^{3}}
$$
$$
c_{\mathrm{P}} \!=\! 3 7. 8 \, \mathrm{~ m o l / m}^{3}
$$
$$
c_{\mathrm{S}} \!=\! 3 6. \, \, \, 3 \, \, \, \mathrm{m o l / m}^{3}
$$
J. $$
c_{\mathrm{A}} \!=\! 1 0. 2 \, \, \, \mathrm{m o l / m^{3}}
$$
$$
c_{\mathrm{P}} \!=\! 3 4. 3 \, \mathrm{~ m o l / m}^{3}
$$
$$
c_{\mathrm{S}} \!=\! 3 4. \, \, \, 2 \, \, \, \mathrm{m o l / m}^{3}
$$
Answer: F
Autocatalytic reaction $\mathrm{A \!+\! P \! \longrightarrow\! P \!+\! P}$: The feed contains 99% of A and 1% of $\mathbf{P}$. The product composition is required to contain 90% of $\mathbf{P}$ and 10% of A. Given $(-r_{\mathrm{A}} )=k c_{\mathrm{A}} c_{\mathrm{P}}$, reaction rate constant $k \!=\! 1.0 \, \mathrm{L} / (\mathrm{min·mol})$, and $c_{\mathrm{A 0}}+c_{\mathrm{P 0}}=1 \, \mathrm{mol/L}$, determine the reaction time required in an ideal batch reactor to achieve the desired product composition is ().

Options:
A. 5.2min
B. 8.0min
C. 6.4min
D. 6.8min
E. 7.8min
F. 5.5min
G. 9.1min
H. 6.0min
I. 8.4min
J. 7.2min
Answer: D
For a first-order reaction with a rate constant $k = 1.0 \ \mathrm{min}^{-1}$, if a conversion rate of 0.9 is required and the reactants are in the same phase, what is the production capacity ratio between a continuous stirred-tank reactor (CSTR) and a batch reactor? For batch operation, the auxiliary production time per batch is $t' = 10 \ \mathrm{min}$.

Options:
A. $$
v_{B}/v_{M}=0.690
$$
B. $$
v_{B}/v_{M}=0.733
$$
C. $$
v_{B}/v_{M}=0.850
$$
D. $$
v_{B}/v_{M}=0.950
$$
E. $$
v_{B}/v_{M}=0.800
$$
F. $$
v_{B}/v_{M}=0.670
$$
G. $$
v_{B}/v_{M}=0.720
$$
H. $$
v_{B}/v_{M}=0.900
$$
I. $$
v_{B}/v_{M}=0.880
$$
J. $$
v_{B}/v_{M}=0.760
$$
Answer: B
In a batch reactor, the following reactions are carried out:
$$
A_{1} \longrightarrow (P + R), \, r_{P} = k_{1}{c_{A}}^{m_1}. \quad A_{2} \longrightarrow S, \, r_{S} = k_{2}{c_{A}}^{m_2}.
$$
Experiments show that at 50°C, $c_{P} / c_{S}$ is consistently equal to 2. After 10 minutes of reaction, the conversion rate of A is 0.50. When the reaction time is doubled, the conversion rate becomes 0.75. Calculate the values of $k_{1}$ and $k_{2}$ is().

Options:
A. $$
k_{1}=0. 0 3 4 2 \operatorname {m i n}^{-1}, k_{2}=0. 0 1 7 5 \operatorname {m i n}^{-1}
$$
B. $$
k_{1}=0. 0 6 1 9 \operatorname {m i n}^{-1}, k_{2}=0. 0 2 8 7 \operatorname {m i n}^{-1}
$$
C. $$
k_{1}=0. 0 3 8 5 \operatorname {m i n}^{-1}, k_{2}=0. 0 1 9 6 \operatorname {m i n}^{-1}
$$
D. $$
k_{1}=0. 0 4 6 2 \operatorname {m i n}^{-1}, k_{2}=0. 0 2 3 1 \operatorname {m i n}^{-1}
$$
E. $$
k_{1}=0. 0 4 9 8 \operatorname {m i n}^{-1}, k_{2}=0. 0 2 5 9 \operatorname {m i n}^{-1}
$$
F. $$
k_{1}=0. 0 5 6 3 \operatorname {m i n}^{-1}, k_{2}=0. 0 3 1 8 \operatorname {m i n}^{-1}
$$
G. $$
k_{1}=0. 0 5 2 7 \operatorname {m i n}^{-1}, k_{2}=0. 0 3 2 4 \operatorname {m i n}^{-1}
$$
H. $$
k_{1}=0. 0 4 3 1 \operatorname {m i n}^{-1}, k_{2}=0. 0 2 0 4 \operatorname {m i n}^{-1}
$$
I. $$
k_{1}=0. 0 5 1 4 \operatorname {m i n}^{-1}, k_{2}=0. 0 2 9 1 \operatorname {m i n}^{-1}
$$
J. $$
k_{1}=0. 0 3 7 8 \operatorname {m i n}^{-1}, k_{2}=0. 0 1 8 9 \operatorname {m i n}^{-1}
$$
Answer: D
The following liquid-phase reactions occur in an isothermal reactor:
$$
A + B → P, \quad r_{\mathrm{P}} = 2 c_{\mathrm{A}}, \, \text{kmol}/(m^{3} \cdot h)
$$
$$
2A → Q, \quad r_{\mathsf{Q}} = 0.5 c_{\mathsf{A}}^{2}, \, \text{kmol}/(m^{3} \cdot h)
$$
The initial concentrations of reactants $A$ and $B$ are 2 $\,\text{kmol}/m^{3}$. After 3 hours of reaction time, what are the conversion rate of $A$ and the yield of $\mathbf{P}$?

Options:
A. $$
x_{A}=0.7500
\\\phi =0.500
$$
B. $$
x_{A}=0.9900
\\\phi =0.650
$$
C. $$
x_{A}=0.9990
\\\phi =0.682
$$
D. $$
x_{A}=0.9700
\\\phi =0.720
$$
E. $$
x_{A}=0.8850
\\\phi =0.612
$$
F. $$
x_{A}=0.9988
\\\phi =0.692
$$
G. $$
x_{A}=0.9100
\\\phi =0.700
$$
H. $$
x_{A}=0.9980
\\\phi =0.500
$$
I. $$
x_{A}=0.8500
\\\phi =0.600
$$
J. $$
x_{A}=0.9500
\\\phi =0.679
$$
Answer: F
Using spherical catalysts with a diameter of 6 mm, a first-order irreversible reaction $\mathrm{A \to P+R}$ is carried out. The molar fraction of $\mathbf{A}$ in the gas-phase bulk is $y_{\Lambda}=0.5$, the operating pressure is $p=0.10133 \, \mathrm{MPa}$, and the reaction temperature is $T=500^\circ \mathrm{C}$. It is known that the rate constant per unit volume of the reactor bed is $0.333 \, \mathrm{s}^{-1}$, the bed porosity is 0.5, the effective diffusivity of component A within the particles is $0.00296 \, \mathrm{cm}^{2}/\mathrm{s}$, and the external mass transfer coefficient is $40 \, \mathrm{m}/\mathrm{h}$. What is the catalyst internal surface utilization rate $\eta_{2}$?

Options:
A. 0.56
B. 0.58
C. 0.42
D. 0.38
E. 0.50
F. 0.52
G. 0.65
H. 0.48
I. 0.45
J. 0.60
Answer: F
Consider the system described by the following state-space equations:
$$
{\left[ \begin{array} {l} {{{\dot{x}_{1}}}} \\ {{{\dot{x}_{2}}}} \\ \end{array} \right]}={\left[ \begin{array} {l l} {{-5}} & {{-1}} \\ {{3}} & {{-1}} \\ \end{array} \right]} {\left[ \begin{array} {l} {{x_{1}}} \\ {{x_{2}}} \\ \end{array} \right]}+{\left[ \begin{array} {l} {{2}} \\ {{5}} \\ \end{array} \right]} u
$$
$$
y=[ 1 \ 2 ] {\left[ \begin{array} {l} {x_{1}} \\ {x_{2}} \\ \end{array} \right]}
$$
What is the transfer function $G(s)$ of this system?

Options:
A. $$
G(s)= \frac{9 s+5 7} {s^{2}+8s+10}
$$
B. $$
G(s)= \frac{2 s+4 8} {s^{2}+5s+7}
$$
C. $$
G(s)= \frac{1 2 s+5 9} {s^{2}+6s+8}
$$
D. $$
G(s)= \frac{1 0 s+3 6} {s^{2}+4s+6}
$$
E. $$
G(s)= \frac{1 1 s+4 5} {s^{2}+3s+5}
$$
F. $$
G(s)= \frac{1 5 s+4 2} {s^{2}+7s+8}
$$
G. $$
G(s)= \frac{2 2 s+6 3} {s^{2}+5s+6}
$$
H. $$
G(s)= \frac{1 4 s+6 2} {s^{2}+7s+9}
$$
I. $$
G(s)= \frac{1 3 s+2 6} {s^{2}+6s+9}
$$
J. $$
G(s)= \frac{8 s+7 9} {s^{2}+9s+11}
$$
Answer: C
Consider the following system under the influence of initial conditions (with no external forcing function):
$$
\begin{array} {c}
\overset \cdots{y} \,+\, 8 \ddot{y} \,+\, 17 \dot y \,+\, 10 y \,=\, 0, \\
y(0) \,=\, 2, \qquad \dot{y}(0) \,=\, 1, \qquad \ddot{y}(0) \,=\, 0.5.
\end{array}
$$
What is the expression for the response $y(t)$ given the initial conditions?

Options:
A. $$y=\begin{bmatrix}0&1&1\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}$$
B. $$y=\begin{bmatrix}1&1&1\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}$$
C. $$y=\begin{bmatrix}0&0&1\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}$$
D. $$y=\begin{bmatrix}1&0&1\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}$$
E. $$y=\begin{bmatrix}1&0&0\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}$$
F. $$y=\begin{bmatrix}1&1&0\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}$$
G. $$y=\begin{bmatrix}1&0&0\end{bmatrix}\begin{bmatrix}x_2\\x_1\\x_3\end{bmatrix}$$
H. $$y=\begin{bmatrix}1&0&0\end{bmatrix}\begin{bmatrix}x_3\\x_2\\x_1\end{bmatrix}$$
I. $$y=\begin{bmatrix}0&1&0\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}$$
J. $$y=\begin{bmatrix}0&0&0\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}$$
Answer: E
Consider the following closed-loop control system:
$$
\frac{C(s)}{R(s)} = \frac{\omega_{n}^{2}}{s^{2} \,+\, 2\zeta\omega_{n}s \,+\, \omega_{n}^{2}}
$$
To make the system's response to a step input signal have approximately 5% overshoot and a settling time of 2 seconds, what is the value of $\omega_{n}$? (Using the 2% tolerance standard.)

Options:
A. $$
w_{n}=3. 2 5 \ r a d / s e c
$$
B. $$
w_{n}=2. 7 0 \ r a d / s e c
$$
C. $$
w_{n}=3. 7 0 \ r a d / s e c
$$
D. $$
w_{n}=3. 5 0 \ r a d / s e c
$$
E. $$
w_{n}=2. 9 0 \ r a d / s e c
$$
F. $$
w_{n}=2. 0 0 \ r a d / s e c
$$
G. $$
w_{n}=4. 2 0 \ r a d / s e c
$$
H. $$
w_{n}=2. 6 0 \ r a d / s e c
$$
I. $$
w_{n}=1. 5 0 \ r a d / s e c
$$
J. $$
w_{n}=3. 0 5 \ r a d / s e c
$$
Answer: E
In the control system,
$$
G(s) = \frac{K \big(s^2 + 6s + 10\big)}{s^2 + 2s + 10}, \qquad H(s) = 1
$$
the root locus of this system is an arc of a circle centered at the origin. What is the radius of the arc?

Options:
A. $$
\sqrt{7} \
$$
B. $$
\sqrt{2 5} \
$$
C. $$
\sqrt{5} \
$$
D. $$
\sqrt{1 2} \
$$
E. $$
\sqrt{1 0} \
$$
F. $$
\sqrt{3 0} \
$$
G. $$
\sqrt{2 0} \
$$
H. $$
\sqrt{1 8} \
$$
I. $$
\sqrt{4} \
$$
J. $$
\sqrt{1 5} \
$$
Answer: E
Consider a closed-loop system with an open-loop transfer function
$$
G(s)H(s) = \frac{K}{s(s+1)(2s+1)}
$$
What is the range of the critical gain $K$ for the system to remain stable?

Options:
A. $$
0 < K < \frac{1} {2}
$$
B. $$
K = \frac{2} {3}$$
C. $$
K < \frac{5} {4}
$$
D. $$
0 < K < \frac{3} {2}
$$
E. $$
K = \frac{5} {6}$$
F. $$
0 < K < \frac{4} {3}
$$
G. $$
K < \frac{7} {2}
$$
H. $$
K > \frac{1} {3}$$
I. $$
0 < K < \frac{1} {3}
$$
J. $$
K > \frac{3} {4}
$$
Answer: D
Consider a unit feedback control system with an open-loop transfer function
$$
G(s) = \frac{a s + 1}{s^{2}}
$$
What is the value of $a$ to make the phase margin equal to 45°?

Options:
A. 0.920
B. 0.780
C. 0.841
D. 0.630
E. 1.100
F. 1.250
G. 1.370
H. 0.950
I. 0.500
J. 1.720
Answer: C
Consider the following state equations and output equation:
$$\begin{bmatrix}\dot{x}_1\\\dot{x}_2\\\dot{x}_3\end{bmatrix}=\begin{bmatrix}-6&1&0\\-11&0&1\\-6&0&0\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}+\begin{bmatrix}2\\6\\2\end{bmatrix}u$$
$$y=\begin{bmatrix}1&0&0\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}$$
By applying an appropriate transformation matrix, the state equations can be converted into the following form:
$$\begin{bmatrix}\dot{z}_1\\\dot{z}_2\\\dot{z}_3\end{bmatrix}=\begin{bmatrix}0&0&-6\\1&0&-11\\0&1&-6\end{bmatrix}\begin{bmatrix}z_1\\z_2\\z_3\end{bmatrix}+\begin{bmatrix}1\\0\\0\end{bmatrix}u$$
Based on $z_{1}, z_{2}$, and $z_{3}$, what is the output $y$?

Options:
A. $$
y=[ \begin{array} {c c c} {{1}} & {{-5}} & {{15}} \\ \end{array} ] \left[ \begin{array} {c} {{{{z_{1}}}}} \\ {{{{z_{2}}}}} \\ {{{{z_{3}}}}} \\ \end{array} \right]
$$
B. $$
y=[ \begin{array} {c c c} {{1}} & {{-5}} & {{10}} \\ \end{array} ] \left[ \begin{array} {c} {{{{z_{1}}}}} \\ {{{{z_{2}}}}} \\ {{{{z_{3}}}}} \\ \end{array} \right]
$$
C. $$
y=[ \begin{array} {c c c} {{2}} & {{-7}} & {{12}} \\ \end{array} ] \left[ \begin{array} {c} {{{{z_{1}}}}} \\ {{{{z_{2}}}}} \\ {{{{z_{3}}}}} \\ \end{array} \right]
$$
D. $$
y=[ \begin{array} {c c c} {{3}} & {{-4}} & {{14}} \\ \end{array} ] \left[ \begin{array} {c} {{{{z_{1}}}}} \\ {{{{z_{2}}}}} \\ {{{{z_{3}}}}} \\ \end{array} \right]
$$
E. $$
y=[ \begin{array} {c c c} {{0}} & {{-3}} & {{11}} \\ \end{array} ] \left[ \begin{array} {c} {{{{z_{1}}}}} \\ {{{{z_{2}}}}} \\ {{{{z_{3}}}}} \\ \end{array} \right]
$$
F. $$
y=[ \begin{array} {c c c} {{4}} & {{-6}} & {{13}} \\ \end{array} ] \left[ \begin{array} {c} {{{{z_{1}}}}} \\ {{{{z_{2}}}}} \\ {{{{z_{3}}}}} \\ \end{array} \right]
$$
G. $$
y=[ \begin{array} {c c c} {{2}} & {{-6}} & {{16}} \\ \end{array} ] \left[ \begin{array} {c} {{{{z_{1}}}}} \\ {{{{z_{2}}}}} \\ {{{{z_{3}}}}} \\ \end{array} \right]
$$
H. $$
y=[ \begin{array} {c c c} {{5}} & {{-8}} & {{13}} \\ \end{array} ] \left[ \begin{array} {c} {{{{z_{1}}}}} \\ {{{{z_{2}}}}} \\ {{{{z_{3}}}}} \\ \end{array} \right]
$$
I. $$
y=[ \begin{array} {c c c} {{2}} & {{-4}} & {{10}} \\ \end{array} ] \left[ \begin{array} {c} {{{{z_{1}}}}} \\ {{{{z_{2}}}}} \\ {{{{z_{3}}}}} \\ \end{array} \right]
$$
J. $$
y=[ \begin{array} {c c c} {{3}} & {{-4}} & {{12}} \\ \end{array} ] \left[ \begin{array} {c} {{{{z_{1}}}}} \\ {{{{z_{2}}}}} \\ {{{{z_{3}}}}} \\ \end{array} \right]
$$
Answer: G
In a single-CPU system with one input device and one output device, there are three concurrently executing tasks. The input, computation, and output times for each task are 2ms, 3ms, and 4ms, respectively, and all follow the order of input, computation, and output. The minimum time required to complete the execution of all three tasks is ().

Options:
A. $$
2 1 \mathrm{m s}
$$
B. $$
1 5 \mathrm{m s}
$$
C. $$
1 3 \mathrm{m s}
$$
D. $$
1 7 \mathrm{m s}
$$
E. $$
1 6 \mathrm{m s}
$$
F. $$
1 4 \mathrm{m s}
$$
G. $$
2 2 \mathrm{m s}
$$
H. $$
1 8 \mathrm{m s}
$$
I. $$
2 0 \mathrm{m s}
$$
J. $$
1 9 \mathrm{m s}
$$
Answer: D
The shared variable definitions and initial values for process $\mathbf{P}_{0}$ and process $\mathbf{P}_{1}$ are: boolean flag[2]; int turn = 0; flag[0] = false; flag[1] = false;
If process $\mathbf{P}_{0}$ and process $\mathbf{P}_{1}$ access the critical resource, the implementation of class $\mathrm{C}$ code is as follows:
void PO() // Process P0
$\{$
while(true)
$\{$
$flag[0]=$ true; turn = 1;
while(flag[1] && (turn == 1)),
critical section;
$flag[0]=$ false;
$\}$
$\}$
void P1() // Process P1
$\{$
while(true)
$\{$
$flag[1]=$ true; turn = 0;
while(flag[0] && (turn == 0))
critical section;
$flag[1]=$ false;
$\}$
$\}$
The result of concurrently executing process $\mathbf{P}_{0}$ and process $\mathbf{P}_{1}$ is ( ) .

Options:
A. Ensures that processes enter the critical section mutually exclusively, preventing the occurrence of "starvation" phenomena.
B. Enables concurrent execution in the critical section, potentially corrupting the shared resources.
C. Alternates process access in a round-robin fashion regardless of critical section completion consistency.
D. Delays both processes indefinitely until they manually reset the shared variables, causing runtime halts.
E. Assumes that both processes have identical execution times, which ensures fair resource utilization.
F. Relies on external synchronization mechanisms besides the shared variables for mutual exclusion guarantees.
G. Permits processes to bypass the critical section entirely, leading to skipped resource access scenarios.
H. Fails to prevent deadlock conditions entirely, resulting in indefinite blocking of processes.
I. Ensures neither mutual exclusion nor fairness, allowing processes to randomly enter the critical section.
J. Allows processes to enter the critical section simultaneously, causing the "starvation" issue to occur occasionally.
Answer: A
The collected partial status data of a computer system employing a demand paging strategy is as follows: CPU utilization is 20%, disk utilization for swap space is 97.7%, and utilization of other devices is 5%. It is determined that the system is experiencing abnormal behavior. Under such circumstances, () can improve system performance.

Options:
A. By reducing the number of running processes
B. By implementing multi-core processing in applications
C. By expanding hard disk capacity to increase swap space
D. By optimizing the power supply for stability
E. By upgrading the CPU to a faster model
F. By increasing the number of active user accounts
G. By installing additional antivirus software
H. By adding more network bandwidth for connectivity
I. By upgrading to a more efficient cooling system
J. By enabling advanced thermal management features
Answer: C
It is known that the system uses a 32-bit physical address, a 48-bit virtual address, a page size of 4KB, a page table entry size of 8B, and the maximum size of each segment is 4GB. If the system adopts segmented paging, how many segments can each user have at most? How many levels of page tables are used within a segment?

Options:
A. $$2^{16}$$
$$4$$
B. $$2^{13}$$
$$4$$
C. $$2^{19}$$
$$4$$
D. $$2^{17}$$
$$4$$
E. $$2^{14}$$
$$3$$
F. $$2^{20}$$
$$3$$
G. $$2^{18}$$
$$3$$
H. $$2^{16}$$
$$3$$
I. $$2^{15}$$
$$2$$
J. $$2^{12}$$
$$5$$
Answer: H
The directory entry of a certain file system is composed of a filename and an index node number. If each directory entry is 64 bytes in length, with 4 bytes used to store the index node number and 60 bytes to store the filename, and the filename consists of lowercase English letters, then the maximum number of files that can be created in this file system is ().

Options:
A. $$2^{64}$$
B. $$2^{20}$$
C. $$2^{28}$$
D. $$2^{16}$$
E. $$2^{12}$$
F. $$2^{8}$$
G. $$2^{48}$$
H. $$2^{32}$$
I. $$2^{60}$$
J. $$2^{24}$$
Answer: H
Assuming the size of a disk block is 1KB, for a 540MB hard disk, how much storage space is the minimum required for its File Allocation Table (FAT)?

Options:
A. $$
1 4 0 0 \mathrm{K B}
$$
B. $$
1 3 5 0 \mathrm{K B}
$$
C. $$
1 4 7 5 \mathrm{K B}
$$
D. $$
1 8 0 0 \mathrm{K B}
$$
E. $$
1 2 0 0 \mathrm{K B}
$$
F. $$
2 0 4 8 \mathrm{K B}
$$
G. $$
1 0 2 4 \mathrm{K B}
$$
H. $$
1 6 0 0 \mathrm{K B}
$$
I. $$
1 1 5 2 \mathrm{K B}
$$
J. $$
1 9 7 5 \mathrm{K B}
$$
Answer: B
The main part of the radish's fleshy root that expands is ____, and the main part of the carrot's fleshy root that expands is ____.

Options:
A. Lateral root, Cortex
B. Epidermis, Pericycle
C. Cambium, Xylem
D. Phloem, Cambium
E. Periderm, Cortex
F. Hypocotyl, Endodermis
G. Cortex, Endodermis
H. Rhizome, Phloem
I. Protoxylem, Pericycle
J. Stele, Hypodermis
Answer: H
The main edible part of radish is ____, while the main edible part of carrot is ____.

Options:
A. Adventitious root, swollen stem
B. Swollen petiole, fibrous root
C. Modified stem, primary root
D. Primary root, fleshy stem
E. Rhizome, edible periderm
F. Enlarged hypocotyl, slender taproot
G. Secondary xylem, fleshy taproot
H. Stem tuber, thickened stem
I. Fibrous root, storage taproot
J. Enlarged cotyledon, storage root
Answer: G
It is advisable to select _____ varieties for the cultivation of spring cabbage.

Options:
A. Narrow-leaf cabbage
B. Round-headed shape
C. Heart-shaped variety
D. Oval-leaf designs
E. Oblong-headed shape
F. Curly-leaf selections
G. Tall-stalk cabbage
H. Spiral-headed shape
I. Conical-headed types
J. Flat-leaf cabbage
Answer: B
In cucumber seedling cultivation, when using ____ for grafting, the cutting direction is () for black-seeded pumpkin and () for the cucumber.

Options:
A. Side-veneer grafting, straight upward, straight downward.
B. Chip budding method, diagonally downward, straight upward.
C. Slit grafting method, horizontally leftward, horizontally rightward.
D. Saddle grafting method, horizontally rightward, horizontally leftward.
E. Hole insertion grafting, straight downward, straight upward.
F. Splice grafting method, diagonally upward, straight downward.
G. Approach grafting method, diagonally downward, diagonally upward.
H. Cleft grafting method, straight downward, diagonally upward.
I. Whip-and-tongue grafting, diagonally upward, diagonally downward.
J. Approach grafting method, straight upward, straight downward.
Answer: G
Brückner referred to his ________ as the "Wagner Symphony."

Options:
A. Symphony No. 5
B. Symphony No. 6
C. Symphony No. 2
D. Symphony No. 1
E. Symphony No. 10
F. Symphony No. 8
G. Symphony No. 7
H. Symphony No. 3
I. Symphony No. 9
J. Symphony No. 4
Answer: D
Suppose the average mass of each of the 7000 asteroids in the solar system is about $1 0^{1 7}$ kg. Compare the total mass of all asteroids with the mass of Earth. The result is ().

Options:
A. 8500
B. 9500
C. 8900
D. 7500
E. 7600
F. 9300
G. 8700
H. 8200
I. 9100
J. 8000
Answer: A
Material at an angular distance of 0.2" from the Galactic center is observed to have an orbital speed of 1200 km/s. If the Sun's distance to the Galactic center is 8 kpc, and the material's orbit is circular and is seen edge-on, calculate the radius of the orbit and the mass of the object around which the material is orbiting is ().

Options:
A. $$
4 5 . 2 \mathrm{~ y r s}
$$
$$
1 . 9 {\times} 1 0^{7} M_{\odot}
$$
B. $$
4 1 . 5 \mathrm{~ y r s}
$$
$$
5 . 7 {\times} 1 0^{6} M_{\odot}
$$
C. $$
4 3 . 8 \mathrm{~ y r s}
$$
$$
7 . 5 {\times} 1 0^{5} M_{\odot}
$$
D. $$
3 3 . 1 \mathrm{~ y r s}
$$
$$
8 . 2 {\times} 1 0^{5} M_{\odot}
$$
E. $$
2 4 . 7 \mathrm{~ y r s}
$$
$$
3 . 1 {\times} 1 0^{5} M_{\odot}
$$
F. $$
3 7 . 4 \mathrm{~ y r s}
$$
$$
1 . 2 {\times} 1 0^{6} M_{\odot}
$$
G. $$
3 9. 8 \mathrm{~ y r s}
$$
$$
2. 6 {\times} 1 0^{6} M_{\odot}
$$
H. $$
2 8 . 9 \mathrm{~ y r s}
$$
$$
3 . 8 {\times} 1 0^{6} M_{\odot}
$$
I. $$
2 9 . 3 \mathrm{~ y r s}
$$
$$
6 . 4 {\times} 1 0^{6} M_{\odot}
$$
J. $$
3 5 . 6 \mathrm{~ y r s}
$$
$$
4 . 9 {\times} 1 0^{7} M_{\odot}
$$
Answer: G
Spectral lines from a Seyfert galaxy are observed to be redshifted by O5 percent and to have broadened emission lines indicating an orbital speed of 250 km/s at an angular distance of 0.1" from its center. Assuming circular orbits, use Kepler's laws to estimate the mass within this 0.1" radius is ().

Options:
A. $$
5. 8 \times 10^{6} \mathrm{~solar~masses}
$$
B. $$
4. 0 \times 10^{7} \mathrm{~solar~masses}
$$
C. $$
2. 5 \times 10^{7} \mathrm{~solar~masses}
$$
D. $$
6. 0 \times 10^{6} \mathrm{~solar~masses}
$$
E. $$
3. 6 \times 10^{8} \mathrm{~solar~masses}
$$
F. $$
2. 3 \times 10^{9} \mathrm{~solar~masses}
$$
G. $$
1. 2 \times 10^{9} \mathrm{~solar~masses}
$$
H. $$
1. 8 \times 10^{8} \mathrm{~solar~masses}
$$
I. $$
7. 9 \times 10^{7} \mathrm{~solar~masses}
$$
J. $$
1. 5 \times1 0^{8} \mathrm{~ s o l a r ~ m a s s e s}
$$
Answer: J
A small satellite galaxy moves in a circular orbit around a much more massive parent and happens to be moving exactly parallel to the line of sight as seen from Earth. The recession welocities of the satellite and the parent galaxy are measured to be 6450 km/s and 6500 km/s, respectively, and the two galaxies are separated by an angle of 0.1° in the sky.Assuming that $H_{o} = 70 km/s/Mpc$, calculate the mass of the parent galaxy is ().

Options:
A. $1. 5 \times1 0^{1 1}$ solar masses
B. $8. 8 \times1 0^{1 0}$ solar masses
C. $1. 0 \times1 0^{1 1}$ solar masses
D. $1. 2 \times1 0^{1 0}$ solar masses
E. $7. 3 \times1 0^{1 0}$ solar masses
F. $9. 4 \times1 0^{1 0}$ solar masses
G. $7. 6 \times1 0^{1 0}$ solar masses
H. $6. 9 \times1 0^{1 0}$ solar masses
I. $5. 4 \times1 0^{1 0}$ solar masses
J. $8. 1 \times1 0^{1 0}$ solar masses
Answer: F
What was the equivalent mass density of the cosmic radiation feld when the universe was one-thousandth its present BE size? (Hint: Dont forget the cosmological redshift!)

Options:
A. $$
5 \times 1 0^{-1 8} \, \frac{k g}{m^{3}}
$$
B. $$
7 \times 1 0^{-1 9} \, \frac{k g}{m^{3}}
$$
C. $$
4 \times 1 0^{-1 8} \, \frac{k g}{m^{3}}
$$
D. $$
6 \times 1 0^{-1 9} \, \frac{k g}{m^{3}}
$$
E. $$
3 \times 1 0^{-2 0} \, \frac{k g}{m^{3}}
$$
F. $$
5 \times 1 0^{-2 0} \, \frac{k g}{m^{3}}
$$
G. $$
1 \times 1 0^{-1 8} \, \frac{k g}{m^{3}}
$$
H. $$
5 \times1 0^{-1 9} \, \frac{k g} {m^{3}}
$$
I. $$
2 \times 1 0^{-1 8} \, \frac{k g}{m^{3}}
$$
J. $$
8 \times 1 0^{-1 9} \, \frac{k g}{m^{3}}
$$
Answer: H
Using the data in the previous problem, how would the inner and outer radii of the Sun's habitable zone change if the solar luminosity increased by a factor of four?

Options:
A. 0.7AU, 2.0AU
B. 0.3AU, 1.2AU
C. 0.2AU, 1.0AU
D. 0.5AU, 1.9AU
E. 0.6AU, 1.5AU
F. 0.8AU, 1.8AU
G. 0.4AU, 1.3AU
H. 0.65AU, 1.6AU
I. 0.9AU, 1.7AU
J. 0.57AU, 1.4AU
Answer: J
Only two isotopes of copper occur naturally, $^{63}Cu$ (atomic mass = 62.9296 amu; abundance 69.17%) and $^{65}Cu$ (atomic mass = 64.9278 amu; abundance 30.83%). Calculate the atomic weight (average atomic mass) of copper.

Options:
A. $$
6 4. 5 3 \mathrm{\ a m u}
$$
B. $$
6 2. 8 5 \mathrm{\ a m u}
$$
C. $$
6 2. 7 0 \mathrm{\ a m u}
$$
D. $$
6 3. 5 5 \mathrm{\ a m u}
$$
E. $$
6 3. 7 1 \mathrm{\ a m u}
$$
F. $$
6 4. 0 1 \mathrm{\ a m u}
$$
G. $$
6 3. 1 9 \mathrm{\ a m u}
$$
H. $$
6 2. 9 4 \mathrm{\ a m u}
$$
I. $$
6 3. 8 0 \mathrm{\ a m u}
$$
J. $$
6 3. 4 9 \mathrm{\ a m u}
$$
Answer: D
A cube of gold that is 1.00 cm on a side has a mass of 19.3 $g$ . A single gold atom has a mass of 197.0 amu. How many gold atoms are in the cube?

Options:
A. $$
5. 3 0 \times1 0^{2 2}
$$
B. $$
4. 8 0 \times1 0^{2 2}
$$
C. $$
6. 4 0 \times1 0^{2 2}
$$
D. $$
5. 1 0 \times1 0^{2 2}
$$
E. $$
7. 7 0 \times1 0^{2 2}
$$
F. $$
6. 8 0 \times1 0^{2 2}
$$
G. $$
5. 9 0 \times1 0^{2 2}
$$
H. $$
4. 5 0 \times1 0^{2 2}
$$
I. $$
7. 1 0 \times1 0^{2 2}
$$
J. $$
3. 9 0 \times1 0^{2 2}
$$
Answer: G
Sodium hydroxide reacts with carbon dioxide as follows:
$$
2 \, \mathrm{N a O H} ( s ) \,+\, \mathrm{C O}_{2} ( g ) \, \longrightarrow\, \mathrm{N a}_{2} \mathrm{C O}_{3} ( s ) \,+\, \mathrm{H}_{2} \mathrm{O} ( l )
$$
Which reagent is the limiting reactant when 1.85 mol NaOH and 1.00 mol $\mathrm{C O_{2}}$ are allowed to react? How many moles of Na2CO3 can be produced? How many moles of the excess reactant remain after the completion of the reaction?

Options:
A. $$ CO_2,0.50mol,1.35mol $$
B. $$
NaOH,0.925mol,0.075mol
$$
C. $$ NaOH,1.00mol,0.85mol $$
D. $$ NaOH,0.50mol,0.500mol $$
E. $$ NaOH,0.925mol,0.125mol $$
F. $$ CO_2,1.00mol,0.850mol $$
G. $$ NaOH,1.85mol,0.00mol $$
H. $$ CO_2,0.925mol,1.075mol $$
I. $$ CO_2,1.00mol,0.075mol $$
J. $$ CO_2,0.875mol,0.150mol $$
Answer: B
An organic compound was found to contain only $\mathrm{C}, \mathrm{H},$ and Cl. When a 1.50-g sample of the compound was completely combusted in air, 3.52 $\mathbf{g}$ of $\mathrm{C O_{2}}$ was formed. In a separate experiment the chlorine in a 1.00-g sample of the compound was converted to 1.27 $\mathbf{g}$ of AgCl. Determine the empirical formula of the compound.

Options:
A. $$
\mathrm{C_{5} H_{5} C l_{2}.}
$$
B. $$
\mathrm{C_{7} H_{7} C l.}
$$
C. $$
\mathrm{C_{6} H_{4} C l_{2}.}
$$
D. $$
\mathrm{C_{6} H_{6} C l_{2}.}
$$
E. $$
\mathrm{C_{8} H_{6} C l.}
$$
F. $$
\mathrm{C_{3} H_{5} C l_{2}.}
$$
G. $$
\mathrm{C_{5} H_{8} C l.}
$$
H. $$
\mathrm{C_{4} H_{7} C l.}
$$
I. $$
\mathrm{C_{4} H_{6} C l.}
$$
J. $$
\mathrm{C_{6} H_{5} C l.}
$$
Answer: J
If an automobile travels 225 mi with a gas mileage of 20.5 mi/gal, how many kilograms of CO$_{2}$ are produced? Assume that the gasoline is composed of octane, $\mathrm{C_{8} H_{1 8} ( l )},$ whose density is 0.69 g/mL.

Options:
A. $$
1 0 0 \, \mathrm{k g} \ \mathrm{C O}_{2}
$$
B. $$
8 5 \, \mathrm{k g} \ \mathrm{C O}_{2}
$$
C. $$
5 0 \, \mathrm{k g} \ \mathrm{C O}_{2}
$$
D. $$
8 0 \, \mathrm{k g} \ \mathrm{C O}_{2}
$$
E. $$
9 5 \, \mathrm{k g} \ \mathrm{C O}_{2}
$$
F. $$
7 5 \, \mathrm{k g} \ \mathrm{C O}_{2}
$$
G. $$
7 0 \, \mathrm{k g} \ \mathrm{C O}_{2}
$$
H. $$
1 1 0 \, \mathrm{k g} \ \mathrm{C O}_{2}
$$
I. $$
6 5 \, \mathrm{k g} \ \mathrm{C O}_{2}
$$
J. $$
9 0 \, \mathrm{k g} \ \mathrm{C O}_{2}
$$
Answer: D
Originally a Central Asian folk dance, the dance movements primarily feature leaps and tap steps. This type of dance is ____.

Options:
A. "The Hu Teng Dance"
B. "The Hu Tong Dance"
C. "The Hun Tang Dance"
D. "The Khan Teng Dance"
E. "The Hu Len Dance"
F. "The Huo Tang Dance"
G. "The Hou Tang Dance"
H. "The Hin Teng Dance"
I. "The Hu Bang Dance"
J. "The Hun Teng Dance"
Answer: A
What are the types of structures in dance drama?

Options:
A. Expression Mode, Performance Mode, Orchestration Mode, Creative Mode
B. Physical Mode, Roleplay Mode, Cadence Mode, Personalized Mode
C. Visual Mode, Interactive Mode, Echo Mode, Original Mode
D. Action Mode, Dialogue Mode, Harmony Mode, Unique Mode
E. Dance Mode, Narrative Mode, Vocal Mode, Traditional Mode
F. Mime Mode, Characterization Mode, Symphony Mode, Custom Mode
G. Movement Mode, Theatrical Mode, Rhythm Mode, Distinct Mode
H. Gesture Mode, Storytelling Mode, Melody Mode, Specialized Mode
I. Artistic Mode, Improvisation Mode, Choral Mode, Adaptive Mode
J. Symbolic Mode, Emotive Mode, Dynamic Mode, Exclusive Mode
Answer: F
What is the title of the theatrical research work written by Yan Changming in the mid-Qianlong period of the Qing Dynasty?

Options:
A. "Scenes of Eastern Harmony"
B. "Essays from the Southern Province"
C. "Reflections on River Rhapsody"
D. "Anthology of Northern Songs"
E. "Stories from the Serene Pines"
F. "Gatherings in the Bamboo Grove"
G. "Chronicles of Mountain Echoes"
H. "Legends of the Flowing Waves"
I. "Selected Works of Qin Yun"
J. "Collection of Lingnan Tales"
Answer: I
Who is the author of the Xijing Trilogy "Xijing Story," "The Great Tree Relocates West," and "The Late-Blooming Rose"?

Options:
A. Mo Yan
B. Shen Congwen
C. Wang Anyi
D. Yan Lianke
E. Lu Xun
F. Wu Cheng'en
G. Su Tong
H. Jia Pingwa
I. Chen Yan
J. Han Shaogong
Answer: I
The molar mass of a certain oil is $120 \ \mathrm{g} \cdot \mathrm{mol}^{-1}$, and its normal boiling point is 473 $\mathrm{K}$. If $1 \; \mathrm{m}^{3}$ of air passes through the oil, assuming the air is at 293 K and $p^{\Theta}$, what is the mass of the oil that escapes with the air?

Options:
A. 8.12g
B. 5.42g
C. 5.96g
D. 8.33g
E. 7.74g
F. 6.27g
G. 6.89g
H. 7.58g
I. 7.01g
J. 9.14g
Answer: H
0.2 mol of $O_{2} (g)$ and 0.5 mol of $N_{2} (g)$ form an ideal mixed gas with a temperature of 298 K and a pressure of 101.325 kPa. What are the partial molar volumes of $O_{2} (g)$ and $N_{2} (g)$, as well as the volume of the mixed gas?

Options:
A. $$
\begin{array} {r c l} {{{}}} & {{}} & {{{V \,=1 7. 7 1 \, d m^{3}}}} \\ \end{array}
$$
$$
V ( \mathrm{O}_{2} ) \;= 2 5 \,. 1 0 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1} \; \;.
$$
$$
V ( \mathrm{N}_{2} ) \,=2 5 \,. 1 0 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1}
$$
B. $$V =17. 12 dm^{3}$$
$$V (O_{2} )= 2445{dm}^{3}\cdot mol^{-1}$$
$$V (N_{2} )=2445{dm}^{3} \cdot {mol}^{-1}$$
C. $$
\begin{array} {r c l} {{{}}} & {{}} & {{{V \,=1 6. 9 5 \, d m^{3}}}} \\ \end{array}
$$
$$
V ( \mathrm{O}_{2} ) \;= 2 4 \,. 6 0 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1} \; \;.
$$
$$
V ( \mathrm{N}_{2} ) \,=2 4 \,. 6 0 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1}
$$
D. $$
\begin{array} {r c l} {{{}}} & {{}} & {{{V \,=2 1. 1 8 \, d m^{3}}}} \\ \end{array}
$$
$$
V ( \mathrm{O}_{2} ) \;= 2 4 \,. 4 0 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1} \; \;.
$$
$$
V ( \mathrm{N}_{2} ) \,=2 4 \,. 4 0 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1}
$$
E. $$
\begin{array} {r c l} {{{}}} & {{}} & {{{V \,=1 9. 0 5 \, d m^{3}}}} \\ \end{array}
$$
$$
V ( \mathrm{O}_{2} ) \;= 2 5 \,. 0 0 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1} \; \;.
$$
$$
V ( \mathrm{N}_{2} ) \,=2 5 \,. 0 0 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1}
$$
F. $$
\begin{array} {r c l} {{{}}} & {{}} & {{{V \,=1 7. 2 5 \, d m^{3}}}} \\ \end{array}
$$
$$
V ( \mathrm{O}_{2} ) \;= 2 4 \,. 5 5 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1} \; \;.
$$
$$
V ( \mathrm{N}_{2} ) \,=2 4 \,. 5 5 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1}
$$
G. $$
\begin{array} {r c l} {{{}}} & {{}} & {{{V \,=1 8. 0 8 \, d m^{3}}}} \\ \end{array}
$$
$$
V ( \mathrm{O}_{2} ) \;= 2 4 \,. 8 0 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1} \; \;.
$$
$$
V ( \mathrm{N}_{2} ) \,=2 4 \,. 8 0 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1}
$$
H. $$
\begin{array} {r c l} {{{}}} & {{}} & {{{V \,=2 0. 3 0 \, d m^{3}}}} \\ \end{array}
$$
$$
V ( \mathrm{O}_{2} ) \;= 2 3 \,. 5 0 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1} \; \;.
$$
$$
V ( \mathrm{N}_{2} ) \,=2 3 \,. 5 0 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1}
$$
I. $$
\begin{array} {r c l} {{{}}} & {{}} & {{{V \,=1 6. 8 9 \, d m^{3}}}} \\ \end{array}
$$
$$
V ( \mathrm{O}_{2} ) \;= 2 3 \,. 9 5 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1} \; \;.
$$
$$
V ( \mathrm{N}_{2} ) \,=2 3 \,. 9 5 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1}
$$
J. $$
\begin{array} {r c l} {{{}}} & {{}} & {{{V \,=1 8. 5 1 \, d m^{3}}}} \\ \end{array}
$$
$$
V ( \mathrm{O}_{2} ) \;= 2 4 \,. 7 5 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1} \; \;.
$$
$$
V ( \mathrm{N}_{2} ) \,=2 4 \,. 7 5 \, \mathrm{d m}^{3} \, \cdot\, \mathrm{m o l}^{-1}
$$
Answer: B
There is currently a ten story dormitory with 10000 numbered rooms on each floor. There are a total of 100 people living in the dormitory, with 10 people allocated to each floor. If we do not consider the names of these 100 people and the maximum number of people per room, how many options are there?

Options:
A. $$
\left[ \frac{1 0 0 0!} {9! 9 9 9 0! 1 0} \right]^{1 0}
$$
B. $$
\left[ \frac{1 0 0 0 0!} {1 0 0! 9 9 9!} \right]^{1 0}
$$
C. $$
\left[ \frac{1 0 0 0!} {1 0! 9 9 9 0 0!} \right]^{1 1}
$$
D. $$
\left[ \frac{1 0 0 0!} {9 9 0! 1 0 0! 9} \right]^{9 9}
$$
E. $$
\left[ \frac{1 0 0 0!} {1 0! 9 9 9 0 0!} \right]^1
$$
F. $$
\left[ \frac{1 0 0! 0 0!} {1 0! 9 9 9!} \right]^{1 0}
$$
G. $$
\left[ \frac{1 0 0 0!} {1 0! 9 9 0 9 9 0!} \right]^{1 0}
$$
H. $$
\left[ \frac{1 0 0 0 0!} {1 0! 9 9 9 0!} \right]^{1 0}
$$
I. $$
\left[ \frac{1 0 0 0!} {1 0! 9 9 0! 9 9} \right]^{1 0 1}
$$
J. $$
\left[ \frac{1 0 0 0!} {1 0! 9 9 0! 1} \right]^{1 0 1}
$$
Answer: H
Let Pb be an Einstein crystal with a vibrational frequency $\nu = 1.9 \times 10^{12} \mathrm{s}^{-1}$. What are the molar vibrational energy (with the zero-point energy at the bottom of the potential energy curve) and the molar heat capacity $C_{V, m}$ at $T = 300 \mathrm{~K}$?

Options:
A. $$
7 9 1 2 \; \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
$$
2 4. 2 7 \; \mathrm{J} \cdot\mathrm{K}^{-1} \cdot\mathrm{m o l}^{-1}
$$
B. $$
7 3 4 9 \; \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
$$
2 5. 9 0 \; \mathrm{J} \cdot\mathrm{K}^{-1} \cdot\mathrm{m o l}^{-1}
$$
C. $$
7 8 5 0 \; \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
$$
2 5. 3 8 \; \mathrm{J} \cdot\mathrm{K}^{-1} \cdot\mathrm{m o l}^{-1}
$$
D. $$
7 6 2 3 \; \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
$$
2 4. 7 6 \; \mathrm{J} \cdot\mathrm{K}^{-1} \cdot\mathrm{m o l}^{-1}
$$
E. $$
7 6 5 8 \; \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
$$
2 2. 4 4 \; \mathrm{J} \cdot\mathrm{K}^{-1} \cdot\mathrm{m o l}^{-1}
$$
F. $$
7 4 2 1 \; \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
$$
2 6. 8 9 \; \mathrm{J} \cdot\mathrm{K}^{-1} \cdot\mathrm{m o l}^{-1}
$$
G. $$
7 6 8 2 \; \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
$$
2 7. 1 2 \; \mathrm{J} \cdot\mathrm{K}^{-1} \cdot\mathrm{m o l}^{-1}
$$
H. $$
7 6 2 3 \; \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
$$
2 3. 4 5 \; \mathrm{J} \cdot\mathrm{K}^{-1} \cdot\mathrm{m o l}^{-1}
$$
I. $$
7 6 0 4 \; \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
$$
2 8. 6 3 \; \mathrm{J} \cdot\mathrm{K}^{-1} \cdot\mathrm{m o l}^{-1}
$$
J. $$
7 7 2 6 \; \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
$$
2 3. 9 0 \; \mathrm{J} \cdot\mathrm{K}^{-1} \cdot\mathrm{m o l}^{-1}
$$
Answer: D
At 298 K, a $0.5 dm^3$ aqueous solution of $NH_4Cl$ with a concentration of $0.200 mol \cdot dm^{-3}$ is mixed with a $0.5 dm^3$ aqueous solution of NaOH with a concentration of $0.100 mol \cdot dm^{-3}$ (ignoring the slight change in volume, and the dissociation constant of $NH_4 OH$ is $K_{b} = 1.8 \times 10^{-5}$). Assume that the activity coefficients of all substances in the solution are equal to 1. What is the concentration of $OH^-$?

Options:
A. $$
7. 2 \times 1 0^{-3} \mathrm{~ m o l ~} \cdot \mathrm{~ d m}^{-3}
$$
B. $$
9. 1 \times 1 0^{-7} \mathrm{~ m o l ~} \cdot \mathrm{~ d m}^{-3}
$$
C. $$
3. 1 \times 1 0^{-6} \mathrm{~ m o l ~} \cdot \mathrm{~ d m}^{-3}
$$
D. $$
1. 8 \times1 0^{-5} \mathrm{~ m o l ~} \cdot\mathrm{~ d m}^{-3}
$$
E. $$
6. 9 \times 1 0^{-5} \mathrm{~ m o l ~} \cdot \mathrm{~ d m}^{-3}
$$
F. $$
2. 5 \times 1 0^{-9} \mathrm{~ m o l ~} \cdot \mathrm{~ d m}^{-3}
$$
G. $$
4. 3 \times 1 0^{-8} \mathrm{~ m o l ~} \cdot \mathrm{~ d m}^{-3}
$$
H. $$
2. 4 \times 1 0^{-5} \mathrm{~ m o l ~} \cdot \mathrm{~ d m}^{-3}
$$
I. $$
5. 6 \times 1 0^{-4} \mathrm{~ m o l ~} \cdot \mathrm{~ d m}^{-3}
$$
J. $$
8. 0 \times 1 0^{-1} \mathrm{~ m o l ~} \cdot \mathrm{~ d m}^{-3}
$$
Answer: D
Given $\phi^{\Theta}( Z\mathrm{h} ^{2+ }: Zn)=-0.763 V$, the overpotential at the Zn cathode when $H_{2}$ begins to evolve is 0.72 V, and it can be assumed that $\eta^(H^+|H_{2},Pt)$ is independent of the concentration of the electrolyte in the solution. To deposit Zn from the solution until the concentration of $Zn^{2+}$ in the solution does not exceed $10^{-4} mol \cdot kg^{-1}$, while ensuring that no $H_2$ evolution occurs during the deposition of $Zn^{2+}$, what is the pH of the solution?

Options:
A. 2.0
B. 2.3
C. 1.7
D. 3.1
E. 1.9
F. 4.0
G. 3.5
H. 2.7
I. 3.8
J. 4.2
Answer: H
A U-tube mercury manometer is used to measure the pressure at a point on the wing of a wind-tunnel model. One side of the manometer is
connected to the model, and the other side is open to the atmosphere. Atmospheric pressure and the density of liquid mercury are $1. 0 1 \times1 0^{5}$ N/m' and $1. 3 6 \times1 0^{4} \mathrm{~ k g / m}^{3}$ , respectively. When the displacement of the two columns of mercury is 20 cm, with the high column on the model side, what is the pressure on the wing?

Options:
A. $$
{8. 5 0 \times1 0^{4} \, \mathrm{N / m}^{2}}
$$
B. $$
{7. 8 3 \times1 0^{4} \, \mathrm{N / m}^{2}}
$$
C. $$
{7. 4 0 \times1 0^{5} \, \mathrm{N / m}^{2}}
$$
D. $$
{7. 5 6 \times1 0^{4} \, \mathrm{N / m}^{2}}
$$
E. $$
{7. 9 9 \times1 0^{4} \, \mathrm{N / m}^{2}}
$$
F. $$
{6. 8 2 \times1 0^{4} \, \mathrm{N / m}^{2}}
$$
G. $$
{7. 0 2 \times1 0^{4} \, \mathrm{N / m}^{2}}
$$
H. $$
{6. 5 4 \times1 0^{4} \, \mathrm{N / m}^{2}}
$$
I. $$
{6. 9 1 \times1 0^{4} \, \mathrm{N / m}^{2}}
$$
J. $$
{7. 4 3 \times1 0^{4} \, \mathrm{N / m}^{2}}
$$
Answer: J
Consider a venturi with a throat-to-inlet area ratio of 0.8, mounted on the side of an airplane fuselage. The airplane is in flight at standard sea level. If the static pressure at the throat is 2100 1b/ft$^{2}$, calculate the velocity of the airplane.

Options:
A. $$
{1 5 2. 1 \, {\mathrm{f t}} / {\mathrm{s e c}}}
$$
B. $$
{1 4 9. 3 \, {\mathrm{f t}} / {\mathrm{s e c}}}
$$
C. $$
{1 5 8. 6 \, {\mathrm{f t}} / {\mathrm{s e c}}}
$$
D. $$
{1 5 6. 9 \, {\mathrm{f t}} / {\mathrm{s e c}}}
$$
E. $$
{1 4 7. 8 \, {\mathrm{f t}} / {\mathrm{s e c}}}
$$
F. $$
{1 6 5. 4 \, {\mathrm{f t}} / {\mathrm{s e c}}}
$$
G. $$
{1 5 4. 7 \, {\mathrm{f t}} / {\mathrm{s e c}}}
$$
H. $$
{1 4 3. 5 \, {\mathrm{f t}} / {\mathrm{s e c}}}
$$
I. $$
{1 6 0. 2 \, {\mathrm{f t}} / {\mathrm{s e c}}}
$$
J. $$
{1 5 0. 8 \, {\mathrm{f t}} / {\mathrm{s e c}}}
$$
Answer: G
The lift on a spinning circular cylinder in a freestream with a velocity of 30 m/s and at standard sea level conditions is 6 N/m of span. Calculate the circulation around the cylinder.

Options:
A. $$
0. 1 3 7 \ \mathrm{m}^{2} / \mathrm{s e c}
$$
B. $$
0. 2 1 5 \ \mathrm{m}^{2} / \mathrm{s e c}
$$
C. $$
0. 0 9 8 \ \mathrm{m}^{2} / \mathrm{s e c}
$$
D. $$
0. 1 8 4 \ \mathrm{m}^{2} / \mathrm{s e c}
$$
E. $$
0. 1 6 3 \ \mathrm{m}^{2} / \mathrm{s e c}
$$
F. $$
0. 1 9 0 \ \mathrm{m}^{2} / \mathrm{s e c}
$$
G. $$
0. 2 0 2 \ \mathrm{m}^{2} / \mathrm{s e c}
$$
H. $$
0. 1 7 5 \ \mathrm{m}^{2} / \mathrm{s e c}
$$
I. $$
0. 1 4 2 \ \mathrm{m}^{2} / \mathrm{s e c}
$$
J. $$
0. 1 5 0 \ \mathrm{m}^{2} / \mathrm{s e c}
$$
Answer: E
The temperature and pressure at the stagnation point of a high-speed missile are 934°R and 7.8 atm, respectively. Calculate the density at this point.

Options:
A. $$
{0. 0 2 5 4 \ \mathrm{s l u g} / \mathrm{f t}^{3}}
$$
B. $$
{0. 0 1 0 3 \ \mathrm{s l u g} / \mathrm{f t}^{3}}
$$
C. $$
{0. 0 0 9 2 \ \mathrm{s l u g} / \mathrm{f t}^{3}}
$$
D. $$
{0. 0 0 5 0 \ \mathrm{s l u g} / \mathrm{f t}^{3}}
$$
E. $$
{0. 0 1 0 9 \ \mathrm{s l u g} / \mathrm{f t}^{3}}
$$
F. $$
{0. 0 1 5 6 \ \mathrm{s l u g} / \mathrm{f t}^{3}}
$$
G. $$
{0. 0 2 0 1 \ \mathrm{s l u g} / \mathrm{f t}^{3}}
$$
H. $$
{0. 0 1 8 9 \ \mathrm{s l u g} / \mathrm{f t}^{3}}
$$
I. $$
{0. 0 2 1 7 \ \mathrm{s l u g} / \mathrm{f t}^{3}}
$$
J. $$
{0. 0 0 8 7 \ \mathrm{s l u g} / \mathrm{f t}^{3}}
$$
Answer: B
In the reservoir of a supersonic wind tunnel, the velocity is negligible, and the temperature is 1000 K. The temperature at the nozzle exit is 600 K. Assuming adiabatic flow through the nozzle, calculate the velocity at the exit.

Options:
A. $$
8 0 0. 0 \mathrm{~ m / s e c}
$$
B. $$
8 6 5. 9 \mathrm{~ m / s e c}
$$
C. $$
9 0 1. 8 \mathrm{~ m / s e c}
$$
D. $$
8 5 6. 2 \mathrm{~ m / s e c}
$$
E. $$
7 8 5. 3 \mathrm{~ m / s e c}
$$
F. $$
8 9 6. 4 \mathrm{~ m / s e c}
$$
G. $$
7 9 9. 9 \mathrm{~ m / s e c}
$$
H. $$
9 8 4. 5 \mathrm{~ m / s e c}
$$
I. $$
9 5 2. 7 \mathrm{~ m / s e c}
$$
J. $$
8 7 2. 0 \mathrm{~ m / s e c}
$$
Answer: F
At a given point in a flow, $T=3 0 0 \mathrm{~ k}$, $p=1. 2$ atm, and $V=2 5 0$ m/s. At this point, calculate the corresponding values of $T_{0}, p_{0}, p^{*}, T^{*}$ , and $M^{*}$ is ().

Options:
A. $$
3 2 8. 0 \mathrm{~^{\circ} K}
$$
$$
1. 6 2 0 \mathrm{~ a t m}
$$
$$
0. 9 0 2 0 \mathrm{~ a t m}
$$
$$
2 7 4^{\circ} \mathrm{K}
$$
$$
0. 8 1
$$
B. $$
3 3 2. 5 \mathrm{~^{\circ} K}
$$
$$
1. 6 8 5 \mathrm{~ a t m}
$$
$$
0. 9 0 1 0 \mathrm{~ a t m}
$$
$$
2 7 5^{\circ} \mathrm{K}
$$
$$
0. 8 2
$$
C. $$
3 2 9. 0 \mathrm{~^{\circ} K}
$$
$$
1. 6 5 0 \mathrm{~ a t m}
$$
$$
0. 8 7 6 5 \mathrm{~ a t m}
$$
$$
2 7 2^{\circ} \mathrm{K}
$$
$$
0. 7 6
$$
D. $$
3 3 0. 0 \mathrm{~^{\circ} K}
$$
$$
1. 6 6 6 \mathrm{~ a t m}
$$
$$
0. 8 9 1 0 \mathrm{~ a t m}
$$
$$
2 7 3^{\circ} \mathrm{K}
$$
$$
0. 8 0
$$
E. $$
3 2 9. 8 \mathrm{~^{\circ} K}
$$
$$
1. 6 8 0 \mathrm{~ a t m}
$$
$$
0. 8 9 5 0 \mathrm{~ a t m}
$$
$$
2 7 7^{\circ} \mathrm{K}
$$
$$
0. 7 9
$$
F. $$
3 3 5. 0 \mathrm{~^{\circ} K}
$$
$$
1. 5 5 4 \mathrm{~ a t m}
$$
$$
0. 8 5 6 3 \mathrm{~ a t m}
$$
$$
2 7 8^{\circ} \mathrm{K}
$$
$$
0. 7 7
$$
G. $$
3 2 0. 1 \mathrm{~^{\circ} K}
$$
$$
1. 7 0 3 \mathrm{~ a t m}
$$
$$
0. 9 0 0 0 \mathrm{~ a t m}
$$
$$
2 8 0^{\circ} \mathrm{K}
$$
$$
0. 8 0
$$
H. $$
3 3 4. 5 \mathrm{~^{\circ} K}
$$
$$
1. 7 1 1 \mathrm{~ a t m}
$$
$$
0. 8 9 9 9 \mathrm{~ a t m}
$$
$$
2 8 1^{\circ} \mathrm{K}
$$
$$
0. 8 3
$$
I. $$
3 3 1. 2 \mathrm{~^{\circ} K}
$$
$$
1. 6 9 4 \mathrm{~ a t m}
$$
$$
0. 8 9 4 6 \mathrm{~ a t m}
$$
$$
2 7 6^{\circ} \mathrm{K}
$$
$$
0. 7 5
$$
J. $$
3 3 3. 2 \mathrm{~^{\circ} K}
$$
$$
1. 6 7 5 \mathrm{~ a t m}
$$
$$
0. 8 8 8 8 \mathrm{~ a t m}
$$
$$
2 7 9^{\circ} \mathrm{K}
$$
$$
0. 7 8
$$
Answer: I
Consider sonic flow. Calculate the maximum deflection angle through which this flow can be expanded via a centered expansion wave.

Options:
A. $$
{1 2 6. 7 5°}
$$
B. $$
{1 3 1. 5 0°}
$$
C. $$
{1 2 8. 3 5°}
$$
D. $$
{1 3 6. 2 5°}
$$
E. $$
{1 3 3. 9 0°}
$$
F. $$
{1 3 5. 6 0°}
$$
G. $$
{1 3 0. 4 5°}
$$
H. $$
{1 2 5. 2 0°}
$$
I. $$
{1 2 7. 8 5°}
$$
J. $$
{1 2 9. 4 5°}
$$
Answer: G
Consider a flat plate at an angle of attack in an inviscid supersonic flow. From linear theory, what is the value of the maximum lift-to-drag ratio, and at what angle of attack does it occur?

Options:
A. $$\frac{1} {\alpha^2}$$
B. $$\frac{1} {\sqrt{\alpha}}$$
C. $$\frac{1} {2\alpha}$$
D. $$\frac{\sqrt{\alpha}} {1}$$
E. $$\frac{\alpha} {1}$$
F. $$\frac{\alpha} {1+\alpha}$$
G. $$\frac{1} {2\alpha^2}$$
H. $$\frac{2} {\alpha}$$
I. $$
\frac{1} {\alpha}
$$
J. $$
\frac{\alpha} {2}$$
Answer: I
A mass of liquid weighs 500 $\mathbf{N}$ when exposed to standard earth's gravity $g=9. 8 0 6 \mathrm{~ m / s^{2} ~}$ .
$$
\mathrm{W h a t ~ i s ~ i t s ~ m a s s?}
$$

Options:
A. $$
5 1. 5 0 \ \mathrm{k g}
$$
B. $$
4 8. 9 9 \ \mathrm{k g}
$$
C. $$
4 7. 5 0 \ \mathrm{k g}
$$
D. $$
5 2. 7 5 \ \mathrm{k g}
$$
E. $$
4 9. 0 1 \ \mathrm{k g}
$$
F. $$
5 0. 9 9 \ \mathrm{k g}
$$
G. $$
5 3. 2 5 \ \mathrm{k g}
$$
H. $$
5 4. 1 0 \ \mathrm{k g}
$$
I. $$
5 2. 0 0 \ \mathrm{k g}
$$
J. $$
5 0. 0 0 \ \mathrm{k g}
$$
Answer: F