MikaStars39/nano-eval huggingface dataset:
The base pressure of a certain engineering pile foundation $p = 120 \text{kPa}$, with the foundation soil being silty clay, has a characteristic value of natural foundation bearing capacity $f_{\mathrm{ak}} = 75 \text{kPa}$. After treatment with vibro-compacted stone columns, a composite foundation is formed. The piles are arranged in an equilateral triangle layout, with a stone column diameter $d = 0.8 \text{m}$ and spacing $s = 1.5 \text{m}$. The ratio of the characteristic value of the natural foundation bearing capacity to the characteristic value of the pile bearing capacity is 1:4, then the characteristic value of the bearing capacity of the composite foundation with vibro-compacted stone columns is ( ) $\text{kPa}$.

Options:
A. 138.7kPa
B. 147.6kPa
C. 110.5kPa
D. 126.4kPa
E. 142.5kPa
F. 133.1kPa
G. 136.2kPa
H. 124.8kPa
I. 102.3kPa
J. 118.9kPa
Answer: F
In a certain site with silty soil, the thickness of the silty soil layer is 10m, with bedrock below 10m. The proposed building on the site will use a raft foundation, with a foundation embedding depth of 2.0m. The additional pressure at the foundation base is 300kPa, and the additional stress at 10m below the surface is 100kPa. The foundation is treated using the powder jet mixing method, with mixing pile diameters of 0.5m and a spacing of 1.5m, arranged in a triangular pattern. The compression modulus of the pile material is 300MPa, and the compression modulus of the soil between piles is 4MPa. The settlement of this raft foundation is ()mm.

Options:
A. 40.7mm
B. 35.4mm
C. 55.6mm
D. 52.8mm
E. 49.0mm
F. 68.1mm
G. 43.7mm
H. 47.2mm
I. 38.5mm
J. 62.3mm
Answer: H
A homogeneous rock slope with a height of 25m uses anchor spraying for support. The standard value of the horizontal component of the lateral rock pressure force (i.e., the unit width rock lateral pressure) is 2000kN/m. If the horizontal spacing of the anchor bolts $s_{\mathrm{x j}}=4.0 \mathrm{m}$ and the vertical spacing $s_{y i}=2.5 \mathrm{m}$, the standard value of the horizontal tensile force on a single anchor bolt is ()kN.

Options:
A. 850kN
B. 1050kN
C. 1000kN
D. 900kN
E. 950kN
F. 750kN
G. 700kN
H. 780kN
I. 820kN
J. 800kN
Answer: J
For a certain first-class building soil slope, permanent anchor retaining walls are used for support. The standard value of the average horizontal earth pressure is $e_{\mathrm{h k}} = 20 \text{kPa}$. The design tensile strength of the anchor bar is $f_{y} = 300 \text{N/mm}^{2}$, with anchor spacing and row distance of 2.0m and 2.5m respectively, and an inclination angle of 20°. The design bond strength between the anchor bar and the grout is $f_{\mathrm{b}} = 2.1 \text{MPa}$, and the characteristic value of bond strength between the anchorage body and the soil is 30kPa. According to the Chinese "Technical Code for Building Slope Engineering" (GB 50330-2002), calculate the required minimum diameter of the anchor bar ()mm.

Options:
A. 35.0mm
B. 33.1mm
C. 27.9mm
D. 25.4mm
E. 32.8mm
F. 29.0mm
G. 34.3mm
H. 30.6mm
I. 31.5mm
J. 28.2mm
Answer: H
A square foundation pit with a side length of 10 meters has a dewatering well placed at each corner. The well group meets the conditions for stable flow of a confined aquifer. The aquifer is 10 meters thick, and the water yield per well is 75 cubic meters per day, with a permeability coefficient of 5 meters per day. The radius of influence of each dewatering well is 90 meters. According to the Chinese "Technical Code for Excavation Support" (JGJ 120-1999), the groundwater level drawdown at the center of the foundation pit is () meters.

Options:
A. 1.76m
B. 3.87m
C. 4.35m
D. 2.91m
E. 2.15m
F. 6.02m
G. 5.04m
H. 3.11m
I. 4.59m
J. 5.08m
Answer: D
The construction site is a sandy soil site located in a seismic intensity zone of 7. The designed basic seismic acceleration is 0.15g, and the seismic design category is Group II. The building adopts a raft foundation with a depth of 3 meters. The groundwater level is at 4.0 meters. The measured standard penetration test blow counts at depths of 5.0 meters, 10.0 meters, and 16.0 meters are 6, 10, and 16, respectively. There is a possibility of liquefaction at () the tested points.

Options:
A. 3
B. 7
C. 9
D. 8
E. 6
F. 11
G. 4
H. 5
I. 12
J. 10
Answer: A
The blood flow velocity through the center of a capillary is $0.066cm/s$, the length of the capillary is $0.1cm$, and its radius $r$ is $2 \times 10^{-4} \mathrm{cm}$. The flow rate $Q$ through the capillary is (). (It is known that the capillary pressure drop is $2600 \mathrm{Pa}$.

Options:
A. $$
4. 1 4 \times1 0^{-9} \mathrm{c m}^{3} / \mathrm{s}
$$
B. $$
5. 6 8 \times1 0^{-8} \mathrm{c m}^{3} / \mathrm{s}
$$
C. $$
2. 0 0 \times1 0^{-8} \mathrm{c m}^{3} / \mathrm{s}
$$
D. $$
6. 2 1 \times1 0^{-8} \mathrm{c m}^{3} / \mathrm{s}
$$
E. $$
7. 4 3 \times1 0^{-9} \mathrm{c m}^{3} / \mathrm{s}
$$
F. $$
3. 3 3 \times1 0^{-9} \mathrm{c m}^{3} / \mathrm{s}
$$
G. $$
3. 5 2 \times1 0^{-9} \mathrm{c m}^{3} / \mathrm{s}
$$
H. $$
9. 9 9 \times1 0^{-7} \mathrm{c m}^{3} / \mathrm{s}
$$
I. $$
1. 8 7 \times1 0^{-7} \mathrm{c m}^{3} / \mathrm{s}
$$
J. $$
2. 9 5 \times1 0^{-8} \mathrm{c m}^{3} / \mathrm{s}
$$
Answer: A
When measuring the magnetic moment of protons using nuclear magnetic resonance, suppose the frequency of the applied alternating magnetic field is $60 \text{MHz}$. Magnetic resonance occurs when the intensity of the direct current magnetic field is adjusted to $1.41 \text{T}$. Given that the proton nuclear spin $I=\frac{1}{2}$, find its magnetic moment and the maximum component in the direction of the magnetic field. (Use $\text{Am}^{2}$ as the unit.)

Options:
A. $2.57 \times 10^{-26} \mathrm{A m}^{2}$
$1.11 \times 10^{-26} \mathrm{A m}^{2}$
B. $2.80 \times 10^{-26} \mathrm{A m}^{2}$
$1.33 \times 10^{-26} \mathrm{A m}^{2}$
C. $2.89 \times 10^{-26} \mathrm{A m}^{2}$
$1.67 \times 10^{-26} \mathrm{A m}^{2}$
D. $3.37 \times 10^{-26} \mathrm{A m}^{2}$
$1.25 \times 10^{-26} \mathrm{A m}^{2}$
E. $2.44 \times1 0^{-2 6} \mathrm{A m}^{2}$
$1. 4 1 \times1 0^{-2 6} \mathrm{A m}^{2}$
F. $2.68 \times 10^{-26} \mathrm{A m}^{2}$
$1.29 \times 10^{-26} \mathrm{A m}^{2}$
G. $2.37 \times 10^{-26} \mathrm{A m}^{2}$
$1.48 \times 10^{-26} \mathrm{A m}^{2}$
H. $1.95 \times 10^{-26} \mathrm{A m}^{2}$
$1.86 \times 10^{-26} \mathrm{A m}^{2}$
I. $3.02 \times 10^{-26} \mathrm{A m}^{2}$
$1.71 \times 10^{-26} \mathrm{A m}^{2}$
J. $2.13 \times 10^{-26} \mathrm{A m}^{2}$
$1.52 \times 10^{-26} \mathrm{A m}^{2}$
Answer: E
An object performing fixed-axis rotation has a moment of inertia $J$ about the axis of rotation. It is initially rotating at a constant angular velocity of $\omega_{0} = 10 \, \mathrm{rad \cdot s^{-1}}$. A constant torque $M = -0.5 \, \mathrm{N \cdot m}$ is then applied to the object. After a time interval of $t = 5.0$ s, the object comes to a stop. The moment of inertia of the object is _______.

Options:
A. $$
J \omega^{2} / 2=2. 1 1 \times1 0^{2 9} \mathrm{J}
$$
B. $$
J \omega^{2} / 2=9. 9 4 \times1 0^{2 5} \mathrm{J}
$$
C. $$
J \omega^{2} / 2=6. 0 2 \times1 0^{2 7} \mathrm{J}
$$
D. $$
J \omega^{2} / 2=9. 4 3 \times1 0^{2 8} \mathrm{J}
$$
E. $$
J \omega^{2} / 2=3. 5 9 \times1 0^{2 6} \mathrm{J}
$$
F. $$
J \omega^{2} / 2=8. 5 1 \times1 0^{2 7} \mathrm{J}
$$
G. $$
J \omega^{2} / 2=1. 8 5 \times1 0^{3 4} \mathrm{J}
$$
H. $$
J \omega^{2} / 2=7. 3 9 \times1 0^{2 8} \mathrm{J}
$$
I. $$
J \omega^{2} / 2=4. 4 7 \times1 0^{3 0} \mathrm{J}
$$
J. $$
J \omega^{2} / 2=5. 0 6 \times1 0^{2 7} \mathrm{J}
$$
Answer: A
In an isolated system, water with a mass of $0.5 \, \mathrm{kg}$ at a temperature of $3^{\circ} \ \mathrm{C}$ and ice with a mass of $0.01 \ \mathrm{kg}$ at a temperature of $0^{\circ} \ \mathrm{C}$ are mixed, resulting in the complete melting of the ice. What is the total change in entropy of the system?

Options:
A. $0. 0 9 \; \mathrm{J} \cdot\mathrm{K}^{-1} = - 0$
B. $0. 0 0 \; \mathrm{J} \cdot\mathrm{K}^{-1} \neq 0$
C. $0. 0 8 \; \mathrm{J} \cdot\mathrm{K}^{-1} > 0$
D. $0. 0 4 \; \mathrm{J} \cdot\mathrm{K}^{-1} \neq 0$
E. $0. 0 5 \; \mathrm{J} \cdot\mathrm{K}^{-1} > 0$
F. $0. 0 7 \; \mathrm{J} \cdot\mathrm{K}^{-1} \neq 0$
G. $0. 0 6 \; \mathrm{J} \cdot\mathrm{K}^{-1} < 0$
H. $0. 0 2 \; \mathrm{J} \cdot\mathrm{K}^{-1} > 0$
I. $0. 0 1 \; \mathrm{J} \cdot\mathrm{K}^{-1} < 0$
J. $0. 0 3 \; \mathrm{J} \cdot\mathrm{K}^{-1} = 0$
Answer: E
At 300 $\mathrm{K}$, how much force is required to stretch a rubber sample to a length of 0.254 m? Assume the initial length of the sample is 0.102 m, the cross-sectional area is $2.58 \times 10^{-5} \mathrm{~ m^{2}}$, the number-average molecular weight before cross-linking $\overline{M_{\mathrm{n}}}=3 \times 10^{4}$, the cross-linked molecular weight $\overline{M_{c}}=6 \times 10^{3}$, and the density at $(300 \mathrm{~K})$ is $9 \times 10^{2} \mathrm{~kg \cdot m^{-3}}$.

Options:
A. $$
1. 3 8 ( \mathrm{k g} )
$$
B. $$
3. 6 5 ( \mathrm{k g} )
$$
C. $$
2. 8 4 ( \mathrm{k g} )
$$
D. $$
2. 2 6 ( \mathrm{k g} )
$$
E. $$
4. 1 2 ( \mathrm{k g} )
$$
F. $$
2. 5 9 ( \mathrm{k g} )
$$
G. $$
1. 7 5 ( \mathrm{k g} )
$$
H. $$
4. 0 3 ( \mathrm{k g} )
$$
I. $$
3. 4 7 ( \mathrm{k g} )
$$
J. $$
1. 9 1 ( \mathrm{k g} )
$$
Answer: A
The photosensitive devices produced by a certain factory have a light intensity sensitivity of $200 \mu A / \mathrm{lm}$ when calibrated with a standard tungsten filament lamp source. Its radiometric sensitivity is ().

Options:
A. $$
4. 1 {\times} 1 0^{3} \ \ ( \mu\mathrm{A} / \mathrm{W} )
$$
B. $$
3. 4 {\times} 1 0^{3} \ \ ( \mu\mathrm{A} / \mathrm{W} )
$$
C. $$
5. 5 {\times} 1 0^{3} \ \ ( \mu\mathrm{A} / \mathrm{W} )
$$
D. $$
5. 0 {\times} 1 0^{3} \ \ ( \mu\mathrm{A} / \mathrm{W} )
$$
E. $$
1. 2 {\times} 1 0^{3} \ \ ( \mu\mathrm{A} / \mathrm{W} )
$$
F. $$
3. 0 {\times} 1 0^{3} \ \ ( \mu\mathrm{A} / \mathrm{W} )
$$
G. $$
4. 7 {\times} 1 0^{3} \ \ ( \mu\mathrm{A} / \mathrm{W} )
$$
H. $$
2. 8 {\times} 1 0^{3} \ \ ( \mu\mathrm{A} / \mathrm{W} )
$$
I. $$
3. 6 {\times} 1 0^{3} \ \ ( \mu\mathrm{A} / \mathrm{W} )
$$
J. $$
2. 5 {\times} 1 0^{3} \ \ ( \mu\mathrm{A} / \mathrm{W} )
$$
Answer: B
Let's consider a thermal detector with a photosensitive area $A_{\mathrm{d}}=1 \, \mathrm{mm}^2$, operating temperature $T=300 \, \mathrm{K}$, and working bandwidth $\Delta f=10 \, \mathrm{Hz}$(Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-12} \, \mathrm{W} \cdot \mathrm{cm}^{-1} \cdot \mathrm{K}^{4}$, Boltzmann constant $k=1.38 \times 10^{-23} \, \mathrm{J} \cdot \mathrm{K}^{-1}$). If the emissivity of the device surface $\varepsilon=1$, the minimum detectable power $P_{\operatorname{min}}$ limited by temperature fluctuations is ().

Options:
A. $$
8. 0 2 {\times} 1 0^{-1 1} \mathrm{W}
$$
B. $$
1. 3 6 {\times} 1 0^{-1 1} \mathrm{W}
$$
C. $$
9. 4 2 {\times} 1 0^{-1 0} \mathrm{W}
$$
D. $$
4. 5 5 {\times} 1 0^{-1 2} \mathrm{W}
$$
E. $$
5. 8 1 {\times} 1 0^{-1 1} \mathrm{W}
$$
F. $$
6. 8 4 {\times} 1 0^{-1 2} \mathrm{W}
$$
G. $$
7. 1 5 {\times} 1 0^{-1 0} \mathrm{W}
$$
H. $$
1. 7 4 {\times} 1 0^{-1 1} \mathrm{W}
$$
I. $$
2. 0 3 {\times} 1 0^{-1 2} \mathrm{W}
$$
J. $$
3. 9 9 {\times} 1 0^{-1 0} \mathrm{W}
$$
Answer: H
A beam of light with a wavelength of 0.5 μm is incident at a 45° angle from the air onto the surface of a medium with a permittivity of $2+j 0.6$. What is the angle of refraction of this light wave in the medium?

Options:
A. $$
\operatorname{a r c s i n} {\frac{2} {5}}
$$
B. $$
\operatorname{a r c s i n} {\frac{2\sqrt{2}} {7}}
$$
C. $$
\operatorname{a r c s i n} {\frac{\sqrt{5}} {5}}
$$
D. $$
\operatorname{a r c s i n} {\frac{\sqrt{6}} {6}}
$$
E. $$
\operatorname{a r c s i n} {\frac{\sqrt{2}} {4}}
$$
F. $$
\operatorname{a r c s i n} {\frac{2\sqrt{2}} {9}}
$$
G. $$
\operatorname{a r c s i n} {\frac{\sqrt{7}} {10}}
$$
H. $$
\operatorname{a r c s i n} {\frac{3} {8}}
$$
I. $$
\operatorname{a r c s i n} {\frac{\sqrt{3}} {4}}
$$
J. $$
\operatorname{a r c s i n} {\frac{1} {2\sqrt{3}}}
$$
Answer: D
At $\mathrm{550nm}$ wavelength, a certain crystal has a $\gamma_{63}$ of $5.5 \times 10^{-12} \mathrm{m} / \mathrm{V}$, and a principal refractive index of 1.58 in the absence of an external field. What is its half-wave voltage?

Options:
A. 23785.7V
B. 11112.7V
C. 15944.1V
D. 22955.3V
E. 18672.6V
F. 17563.4V
G. 12676.5V
H. 10476.8V
I. 19864.2V
J. 14233.9V
Answer: G
Select the LiNbO$_3$ crystal as the intracavity frequency-doubling crystal. Assume the laser working material is Nd$^{3+}$:YAG, then the fundamental wavelength $\lambda = 1.06\mu m$, spectral linewidth $\Delta\nu = 1.35\times10^{11}$ Hz, average diameter of the fundamental beam $a = 2$ mm, single-pass loss $a_{i} = 2\times10^{-2}$, refractive index of $\mathrm{(LiNbO_3)n_1 \approx n_2 \approx n_3 \approx 2.2}$, nonlinear coefficient $d = 5\times10^{-23}$ (in MKS units). What is the optimal length for the $\mathrm{LiNbO_3}$ crystal?

Options:
A. 29.5μm
B. 39.9μm
C. 38.6μm
D. 31.8μm
E. 42.7μm
F. 47.6μm
G. 44.3μm
H. 28.4μm
I. 50.1μm
J. 35.2μm
Answer: C
To achieve an η of 1.7 for uranium, what should be the enrichment level of U-235 in uranium (E=0.0253 eV)?

Options:
A. $$
N ( U 8 )=5 1. 6 N ( U 5 )
$$
B. $$
N ( U 8 )=5 4. 9 N ( U 5 )
$$
C. $$
N ( U 8 )=5 5. 8 N ( U 5 )
$$
D. $$
N ( U 8 )=6 0. 3 N ( U 5 )
$$
E. $$
N ( U 8 )=4 8. 7 N ( U 5 )
$$
F. $$
N ( U 8 )=5 0. 2 N ( U 5 )
$$
G. $$
N ( U 8 )=5 3. 4 N ( U 5 )
$$
H. $$
N ( U 8 )=6 1. 2 N ( U 5 )
$$
I. $$
N ( U 8 )=5 9. 1 N ( U 5 )
$$
J. $$
N ( U 8 )=4 9. 5 N ( U 5 )
$$
Answer: B
In a certain nuclear reactor, the neutron density varies as $n(t) = A_{0} \mathrm{e}^{\omega_{1} t} + A_{1} \mathrm{e}^{\omega_{2} t}$. What is the period of this nuclear reactor?

Options:
A. $$
T ( t )=\frac{A_{0} \mathbf{e}^{\omega_{1} t}+A_{1} \mathbf{e}^{\omega_{2} t}} {A_{0} \omega_{1} \mathbf{e}^{\omega_{1} t}+A_{1} \omega_{2} \mathbf{e}^{\omega_{2} t}}
$$
B. $$
T ( t )=\frac{A_{1} \omega_{2} \mathbf{e}^{\omega_{2} t}-A_{0} \omega_{1} \mathbf{e}^{\omega_{1} t}} {A_{1} \mathbf{e}^{\omega_{2} t}-A_{0} \mathbf{e}^{\omega_{1} t}}
$$
C. $$
T ( t )=\frac{A_{0} \omega_{1} \mathbf{e}^{\omega_{1} t}+A_{1} \omega_{2} \mathbf{e}^{\omega_{2} t}} {A_{0} \mathbf{e}^{2 \omega_{1} t}+A_{1} \mathbf{e}^{2 \omega_{2} t}}
$$
D. $$
T ( t )=\frac{A_{1} \mathbf{e}^{\omega_{2} t}+A_{0} \mathbf{e}^{-\omega_{1} t}} {A_{1} \omega_{2} \mathbf{e}^{\omega_{2} t}+A_{0} \omega_{1} \mathbf{e}^{-\omega_{1} t}}
$$
E. $$
T ( t )=\frac{A_{0} \omega_{2} \mathbf{e}^{\omega_{2} t}+A_{1} \omega_{1} \mathbf{e}^{\omega_{1} t}} {A_{1} \mathbf{e}^{-\omega_{1} t}-A_{0} \mathbf{e}^{-\omega_{2} t}}
$$
F. $$
T ( t )=\frac{\omega_{1} A_{0} \mathbf{e}^{\omega_{1} t}+\omega_{2} A_{1} \mathbf{e}^{\omega_{2} t}} {A_{0} \mathbf{e}^{-\omega_{1} t}+A_{1} \mathbf{e}^{-\omega_{2} t}}
$$
G. $$
T ( t )=\frac{A_{1} \mathbf{e}^{\omega_{1} t}+A_{0} \mathbf{e}^{\omega_{2} t}} {A_{1} \omega_{1} \mathbf{e}^{\omega_{1} t}+A_{0} \omega_{2} \mathbf{e}^{\omega_{2} t}}
$$
H. $$
T ( t )=\frac{A_{0} \mathbf{e}^{2 \omega_{2} t}+A_{1} \mathbf{e}^{2 \omega_{1} t}} {A_{0} \omega_{1} \mathbf{e}^{\omega_{1} t}-A_{1} \omega_{2} \mathbf{e}^{\omega_{2} t}}
$$
I. $$
T ( t )=\frac{\omega_{2} A_{1} \mathbf{e}^{\omega_{1} t}-\omega_{1} A_{0} \mathbf{e}^{\omega_{2} t}} {A_{1} \mathbf{e}^{2 \omega_{2} t}+A_{0} \mathbf{e}^{2 \omega_{1} t}}
$$
J. $$
T ( t )=\frac{A_{0} \omega_{1} \mathbf{e}^{\omega_{1} t}-A_{1} \omega_{2} \mathbf{e}^{\omega_{2} t}} {A_{0} \mathbf{e}^{\omega_{1} t}+A_{1} \mathbf{e}^{\omega_{2} t}}
$$
Answer: A
Ideal for chillers, cold air absorbs heat at a constant pressure in cold air between 72K and 88K and expels heat isothermally at 300K.Assuming the working fluid is an ideal gas, with the working substance being compressed from 88K to 300K and expanded from 300K to 72K as an isentropic process, and the isentropic index is $1.4$. Try to find the coefficient of performance of the refrigerator.

Options:
A. 0.0812
B. 0.0755
C. 0.1250
D. 0.0785
E. 0.0700
F. 0.0450
G. 0.0543
H. 0.0927
I. 0.0999
J. 0.0630
Answer: B
Calculate the intermediate pressure $p_m$ for a single-stage throttling, fully cooled at the intermediate stage, two-stage expansion ammonia refrigeration cycle with a working temperature of $t_{k}=38^{\circ}\mathrm{C}, t_{0}=-33.33^{\circ}\mathrm{C}$. Here,
The low-pressure compressor has a theoretical discharge volume $q_{V t L}=566 \, \mathrm{m}^{3} / \mathrm{h}$ for one unit.
The high-pressure compressor has a theoretical discharge volume $q_{V \mathrm{t H}}=283 \, \mathrm{m}^{3} / \mathrm{h}$ for one unit.

Options:
A. $$
0. 4 4 4 4 \mathrm{M P a}
$$
B. $$
0. 3 9 6 2 \mathrm{M P a}
$$
C. $$
0. 4 0 2 5 \mathrm{M P a}
$$
D. $$
0. 3 5 5 5 \mathrm{M P a}
$$
E. $$
0. 1 3 9 8 \mathrm{M P a}
$$
F. $$
0. 1 8 3 6 \mathrm{M P a}
$$
G. $$
0. 2 5 5 0 \mathrm{M P a}
$$
H. $$
0. 2 1 6 7 \mathrm{M P a}
$$
I. $$
0. 3 1 7 7 \mathrm{M P a}
$$
J. $$
0. 2 7 8 4 \mathrm{M P a}
$$
Answer: I
The mole fractions of the components in the mixture are: 78% $\mathrm{N_{2}}$, 20% $\mathrm{O_{2}}$, and 2% Ar, at a temperature of 300K. All three gases are ideal gases.
Assuming only $\mathrm{Ar}$ is separated from $\mathrm{N_{2}}+\mathrm{O_{2}}+\mathrm{Ar}$, while $\mathrm{N_{2}}+\mathrm{O_{2}}$ remain mixed, calculate the specific work required for the reversible isothermal separation of argon.

Options:
A. $$301kJ/kg$$
B. $$290kJ/kg$$
C. $$315kJ/kg$$
D. $$317kJ/kg$$
E. $$318kJ/kg$$
F. $$299kJ/kg$$
G. $$295kJ/kg$$
H. $$306kJ/kg$$
I. $$320kJ/kg$$
J. $$312kJ/kg$$
Answer: H
Given a spherical soap bubble with a diameter of 0.1 cm. Assume the pressure of the air surrounding the soap bubble is $1.013 \times 10^{s} \mathrm{Pa}$, and the surface tension coefficient at the water-air interface is $\alpha = 72 \times 10^{-5} \mathrm{N/m}$. The air pressure $p$ inside the soap bubble is ( ) .

Options:
A. 101500Pa.
B. 101320Pa.
C. 101140Pa.
D. 101588Pa
E. 101482Pa.
F. 101398Pa.
G. 101670Pa.
H. 101177Pa.
I. 101360Pa.
J. 101290Pa.
Answer: D
In a uniformly flowing field, place an isolated point source, with the incoming flow velocity denoted as $U$ and the point source strength as $Q$. The fluid is ideal and incompressible. What is the shape of the streamline ?

Options:
A. $$
\frac{Q} {2 \pi} \, r \operatorname{sin} \theta-U r^{2} \operatorname{sin}^{2} \theta = \text{constant}
$$
B. $$
\frac{1} {2} \, Q r \operatorname{cos} \theta+\frac{U} {4 \pi} \operatorname{sin} \theta = \text{constant}
$$
C. $$
\frac{U} {4 \pi} r \operatorname{cos} \theta-\frac{Q} {2} \operatorname{sin} \theta = \text{constant}
$$
D. $$
\frac{1} {2} \, U r^{2} \operatorname{cos} \theta-\frac{Q} {4 \pi} \operatorname{sin} \theta = \text{constant}
$$
E. $$
-U r^{2} \operatorname{cos} \theta+\frac{Q} {2 \pi} \operatorname{cos} \theta^{2} = \text{constant}
$$
F. $$
U r \operatorname{cos} \theta+\frac{Q} {2 \pi} \operatorname{sin} \theta^{2} = \text{constant}
$$
G. $$
\frac{1} {4} \, Q r \operatorname{sin} \theta-\frac{U} {2 \pi} \operatorname{cos}^{2} \theta = \text{constant}
$$
H. $$
\frac{1} {4} \, U r^{2} \operatorname{cos} \theta-\frac{Q} {2 \pi} \operatorname{cos} \theta = \text{constant}
$$
I. $$
\frac{1} {2} \, U r^{2} \operatorname{sin} \theta-\frac{Q} {4 \pi} \operatorname{cos} \theta = \text{constant}
$$
J. $$
\frac{1} {3} \, U r^{3} \operatorname{sin} \theta+\frac{Q} {4 \pi} \operatorname{cos}^{2} \theta = \text{constant}
$$
Answer: I
A shaft with a diameter of $d = 10 \, \mathrm{cm}$ operates unloaded in a bearing, with a rotational speed of $n = 5000 \, \text{r/min}$ (revolutions per minute). The shaft and bearing are concentric, with a radial clearance of $\delta = 0.005 \, \mathrm{cm}$, and the length of the bearing is $l = 8 \, \mathrm{cm}$. The measured frictional torque is $M = 3.5 \, \mathrm{N} \cdot \mathrm{m}$. What is the shear stress in the fluid between the shaft and the bearing ?

Options:
A. $$
3 2 7 9 \mathrm{P a}
$$
B. $$
1 5 3 2 \mathrm{P a}
$$
C. $$
2 9 1 6 \mathrm{P a}
$$
D. $$
2 7 8 5 \mathrm{P a}
$$
E. $$
2 3 7 8 \mathrm{P a}
$$
F. $$
1 8 6 4 \mathrm{P a}
$$
G. $$
2 0 8 9 \mathrm{P a}
$$
H. $$
3 4 5 0 \mathrm{P a}
$$
I. $$
3 9 4 1 \mathrm{P a}
$$
J. $$
4 5 6 7 \mathrm{P a}
$$
Answer: D
The density distribution of a thin, straight rod is $\rho = \rho_0 (a + l)$ ($\rho_0$ and $a$ are constants, $l$ is the distance measured from one end of the rod). The rod is floating vertically in a certain liquid. If the total length of the rod is $L$, and the volume of the portion of the rod above the liquid surface is $\frac{1}{n}$ of the $\textbf{Total volume of the rod}$, $\textbf{determine the density of the liquid}$ is().

Options:
A. $$
\rho_{0} \, \frac{n} {n+1} \Bigl( a+\frac{l} {2} \Bigr)
$$
B. $$
\rho_{0} \, \frac{n} {n-1} \Bigl( a+\frac{1} {l} \Bigr)
$$
C. $$
\rho_{0} \, \frac{n+1} {n-1} \Bigl( a+\frac{l} {2} \Bigr)
$$
D. $$
\rho_{0} \, \frac{2n} {n-1} \Bigl( a+\frac{l} {3} \Bigr)
$$
E. $$
\rho_{0} \, \frac{n} {2(n-1)} \Bigl( a+\frac{l} {3} \Bigr)
$$
F. $$
\rho_{0} \, \frac{n} {2(n-1)} \Bigl( a+\frac{2l} {3} \Bigr)
$$
G. $$
\rho_{0} \, \frac{n^2} {n-1} \Bigl( a+\frac{l} {2} \Bigr)
$$
H. $$
\rho_{0} \, \frac{n} {n-1} \Bigl( a+\frac{l} {2} \Bigr)
$$
I. $$
\rho_{0} \, \frac{n} {n+1} \Bigl( a+\frac{2l} {3} \Bigr)
$$
J. $$
\rho_{0} \, \frac{n} {n-1} \Bigl( a+\frac{3l} {4} \Bigr)
$$
Answer: H
Consider a thin layer of fluid with non-uniform heating that adheres closely to the surface of a horizontal solid plane. Within the plane of the fluid layer, the temperature is a known function of the horizontal coordinate $x$. Because the fluid layer is very thin, it can be assumed to be independent of the coordinate $z$ that passes through the fluid layer. Non-uniform heating causes steady flow within the layer, resulting in a variation of the layer's thickness $\zeta$ in the $x$ direction. Determine the function $\zeta(x)$.

Options:
A. $$
2 \rho^{-2 / 5} \Bigl( \int \rho^{-3 / 8} \, \mathrm{d} \theta + \text{constant} \Bigl)
$$
B. $$
3 \rho^{-2 / 3} \Bigl( \int \rho^{-2 / 7} \, \mathrm{d} \psi + \text{constant} \Bigl)
$$
C. $$
5 \rho^{-1} \Bigl( \int \rho^{-3 / 4} \, \mathrm{d} \delta + \text{constant} \Bigl)
$$
D. $$
6 \rho^{-1 / 4} \Bigl( \int \rho^{-1 / 5} \, \mathrm{d} \phi + \text{constant} \Bigl)
$$
E. $$
3 \rho^{-3 / 8} \Bigl( \int \rho^{-1 / 2} \, \mathrm{d} \kappa + \text{constant} \Bigl)
$$
F. $$
2 \rho^{-2 / 3} \Bigl( \int \rho^{0} \, \mathrm{d} \beta + \text{constant} \Bigl)
$$
G. $$
4 \rho^{-4 / 9} \Bigl( \int \rho^{-4 / 9} \, \mathrm{d} \lambda + \text{constant} \Bigl)
$$
H. $$
4 \rho^{-1 / 2} \Bigl( \int \rho^{-1 / 2} \, \mathrm{d} \gamma + \text{constant} \Bigl)
$$
I. $$
3 \rho^{-5 / 6} \Bigl( \int \rho^{-1 / 3} \, \mathrm{d} \epsilon + \text{constant} \Bigl)
$$
J. $$
\rho \zeta^2 = 3 \rho^{-3 / 4} \Bigl( \int \rho^{-1 / 4} \, \mathrm{d} \alpha + \text{constant} \Bigl)
$$
Answer: J
Let the reset potential be
$$
w ( z )=( 1+i ) \ln \left( z^{i}+1 \right)+( 2-3 i ) \ln \left( z^{i}+4 \right)+\frac{1} {z},
$$
calculate the fluid volume flow rate $Q$ through the circle $x^{2}+y^{2} \leq9$.

Options:
A. $$
1 2 \pi
$$
B. $$
6 2 \pi
$$
C. $$
1 0 \pi
$$
D. $$
-1 2 \pi
$$
E. $$
3 2 \pi
$$
F. $$
1 3 \pi
$$
G. $$
4 2 \pi
$$
H. $$
1 5 \pi
$$
I. $$
1 2 \gamma
$$
J. $$
0 2 \pi
$$
Answer: A
Consider the irrotational flow of an ideal incompressible fluid in the semi-infinite space $x > 0$. If there is an isolated point source with strength $Q$ at the point $(x_{0}, y_{0}, z_{0})$, give the velocity potential.

Options:
A. $$
- \frac{2Q} {4 \pi} \biggl[ \frac{1} {\sqrt{( x-x_{0} )^{2}+( y+y_{0} )^{2}+( z-z_{0} )^{2}}}
$$
$$
+ \frac{1} {\sqrt{( x+x_{0} )^{2}+( y-y_{0} )^{2}+( z+z_{0} )^{2}}}
$$
B. $$
\frac{Q} {4 \pi} \biggl[ \frac{1} {\sqrt{( x-x_{0} )^{2}+( y-y_{0} )^{2}+( z-z_{0} )^{2}}}
$$
$$
- \frac{1} {\sqrt{( x+x_{0} )^{2}+( y-y_{0} )^{2}+( z-z_{0} )^{2}}}
$$
C. $$
- \frac{Q} {4 \pi} \biggl[ \frac{2} {\sqrt{( x-x_{0} )^{2}+( y-y_{0} )^{2}+( z-z_{0} )^{2}}}
$$
$$
+ \frac{1} {\sqrt{( x+x_{0} )^{2}+( y+y_{0} )^{2}+( z-z_{0} )^{2}}}
$$
D. $$
- \frac{Q} {4 \pi} \biggl[ \frac{1} {\sqrt{( x+x_{0} )^{2}+( y-y_{0} )^{2}+( z-z_{0} )^{2}}}
$$
$$
+ \frac{1} {\sqrt{( x-x_{0} )^{2}+( y+y_{0} )^{2}+( z+z_{0} )^{2}}}
$$
E. $$
- \frac{Q} {4 \pi} \biggl[ \frac{1} {\sqrt{( x-x_{0} )^{2}+( y-y_{0} )^{2}+( z-z_{0} )^{2}}}
$$
$$
+ \frac{1} {\sqrt{( x+x_{0} )^{2}+( y-y_{0} )^{2}+( z-z_{0} )^{2}}} \bigg]
$$
F. $$
- \frac{Q} {4 \pi} \biggl[ \frac{1} {\sqrt{( x-x_{0} )^{2}+( y-y_{0} )^{2}+( z+z_{0} )^{2}}}
$$
$$
+ \frac{1} {\sqrt{( x-x_{0} )^{2}+( y+y_{0} )^{2}+( z-z_{0} )^{2}}}
$$
G. $$
- \frac{Q} {8 \pi} \biggl[ \frac{1} {\sqrt{( x-x_{0} )^{2}+( y-y_{0} )^{2}+( z-z_{0} )^{2}}}
$$
$$
+ \frac{1} {\sqrt{( x+x_{0} )^{2}+( y-y_{0} )^{2}+( z+z_{0} )^{2}}}
$$
H. $$
- \frac{Q} {2 \pi} \biggl[ \frac{1} {\sqrt{( x-x_{0} )^{2}+( y+y_{0} )^{2}+( z+z_{0} )^{2}}}
$$
$$
+ \frac{1} {\sqrt{( x+x_{0} )^{2}+( y-y_{0} )^{2}+( z-z_{0} )^{2}}}
$$
I. $$
\frac{Q} {4 \pi} \biggl[ \frac{1} {\sqrt{( x-x_{0} )^{2}+( y-y_{0} )^{2}+( z-z_{0} )^{2}}}
$$
$$
+ \frac{1} {\sqrt{( x-x_{0} )^{2}+( y+y_{0} )^{2}+( z+z_{0} )^{2}}}
$$
J. $$
\frac{Q} {2 \pi} \biggl[ \frac{1} {\sqrt{( x-x_{0} )^{2}+( y-y_{0} )^{2}+( z-z_{0} )^{2}}}
$$
$$
- \frac{1} {\sqrt{( x+x_{0} )^{2}+( y-y_{0} )^{2}+( z+z_{0} )^{2}}}
$$
Answer: E
A certain carbon chain poly $\alpha$-olefin, with an average relative molecular mass $M = 1 \, 0 0 0 \, M_{0}$ ($M_{0}$ is the relative molecular mass of the chain segment), calculate the elastic limit of this polymer $( L_{\operatorname* {m a x}} / ( ( r^{2} )_{f, \, r} )^{1 / 2} )$?

Options:
A. 33.7
B. 23.1
C. 22.5
D. 25.9
E. 13.4
F. 18.2
G. 27.3
H. 29.6
I. 41.8
J. 35.9
Answer: D
The electromotive force of the battery Zn|ZnCl(0.05 mol/dm$^{3}$), AgCl(solid)|Ag at 25°C is 1.015 V, and the temperature coefficient of the electromotive force is $- 4.92 \times 10^{-4}$ V/K. The change in Gibbs free energy, the heat effect of the reaction, and the change in entropy for the battery reaction is().

Options:
A. $$
=-2 3 5. 1 ~ \mathrm{k J} / \mathrm{m o l}
$$
B. $$
=-2 2 8. 5 ~ \mathrm{k J} / \mathrm{m o l}
$$
C. $$
=-2 3 1. 8 ~ \mathrm{k J} / \mathrm{m o l}
$$
D. $$
=-2 3 2. 4 ~ \mathrm{k J} / \mathrm{m o l}
$$
E. $$
=-2 4 0. 0 ~ \mathrm{k J} / \mathrm{m o l}
$$
F. $$
=-2 2 9. 3 ~ \mathrm{k J} / \mathrm{m o l}
$$
G. $$
=-2 1 5. 9 ~ \mathrm{k J} / \mathrm{m o l}
$$
H. $$
=-2 2 4. 2 ~ \mathrm{k J} / \mathrm{m o l}
$$
I. $$
=-2 3 0. 6 ~ \mathrm{k J} / \mathrm{m o l}
$$
J. $$
=-2 1 6. 7 ~ \mathrm{k J} / \mathrm{m o l}
$$
Answer: H
The cell $\mathrm{Zn} \mid \mathrm{ZnCl}_{2} \left( m \right), \, \mathrm{Hg}_{2} \mathrm{Cl}_{2} (\text{solid}) \mid \mathrm{Hg}$ at 25°C: (a) When $m = 0.25148$ mol/kg, the electromotive force $E = 1.10085 \, \mathbf{V}$. (b) When $m = 0.0050$ mol/kg, the electromotive force is $1.2244 \, \mathrm{V}$. The ratio of the mean ionic activity coefficients of the two $\text{ZnCl}_{2}$ solutions is().

Options:
A. $$
\frac{\gamma_{\pm, a}} {\gamma_{\pm, b}}=0. 9 0
$$
B. $$
\frac{\gamma_{\pm, a}} {\gamma_{\pm, b}}=0. 8 1
$$
C. $$
\frac{\gamma_{\pm, a}} {\gamma_{\pm, b}}=1. 2 5
$$
D. $$
\frac{\gamma_{\pm, a}} {\gamma_{\pm, b}}=1. 0 7
$$
E. $$
\frac{\gamma_{\pm, a}} {\gamma_{\pm, b}}=0. 6 2
$$
F. $$
\frac{\gamma_{\pm, a}} {\gamma_{\pm, b}}=0. 5 5
$$
G. $$
\frac{\gamma_{\pm, a}} {\gamma_{\pm, b}}=1. 1 3
$$
H. $$
\frac{\gamma_{\pm, a}} {\gamma_{\pm, b}}=0. 7 3
$$
I. $$
\frac{\gamma_{\pm, a}} {\gamma_{\pm, b}}=0. 4 9
$$
J. $$
\frac{\gamma_{\pm, a}} {\gamma_{\pm, b}}=1. 3 4
$$
Answer: I
Electrolyze a mixed solution of 1 mol/L HSOa and 0.1 mol/L Cu$SO_{\mathrm{4}}$. When the concentration of $\mathrm{Cu^{2+}}$ ions has decreased to $10^{-7}$ mol/L, what is the potential of the cathode? Given that the overpotential for hydrogen evolution on copper is 0.23V, what is the minimum cathode potential achievable without hydrogen evolution?

Options:
A. $$
\approx-0. 3 3 V
$$
B. $$
\approx-0. 1 9 V
$$
C. $$
\approx-0. 3 5 V
$$
D. $$
\approx-0. 1 8 V
$$
E. $$
\approx-0. 2 8 V
$$
F. $$
\approx-0. 1 5 V
$$
G. $$
\approx-0. 2 2 V
$$
H. $$
\approx-0. 2 9 V
$$
I. $$
\approx-0. 3 1 V
$$
J. $$
\approx-0. 3 8 V
$$
Answer: E
At 25°C, in a stagnant solution, the cathodic reaction $\mathrm{Cu^{2+} + 2e \to Cu}$ is controlled by the diffusion step. The diffusion coefficient of $\mathrm{Cu^{2+}}$ ions in this solution is $1 \times 10^{-5} \mathrm{cm}^{2}/\mathrm{s}$, and the effective thickness of the diffusion layer is $1.1 \times 10^{-2} \mathrm{cm}$. The concentration of $\mathrm{Cu^{2+}}$ ions is 0.5 mol/L. The concentration polarization value when the cathode current density is 0.044 A/cm² is().

Options:
A. $$
=-13 m V
$$
B. $$
=-7 m V
$$
C. $$
=-14 m V
$$
D. $$
=-8 m V
$$
E. $$
=-6 m V
$$
F. $$
=-9 m V
$$
G. $$
=-10 m V
$$
H. $$
=-11 m V
$$
I. $$
=-12 m V
$$
J. $$
=-15 m V
$$
Answer: F
At 20°C, the exchange current density of nickel in a 1 mol/L NiSO₄ solution is $2 \times 10^{-9} \mathrm{A/cm}^{2}$. When nickel is electrodeposited at a current density of 0.04 A/cm², electrochemical polarization occurs at the cathode. If the transfer coefficient $\overrightarrow{\alpha} = 1.0$, what is the cathode potential?

Options:
A. $$
= 0. 4 2 4 V
$$
B. $$
= 0. 2 7 4 V
$$
C. $$
= 0. 4 8 9 V
$$
D. $$
= 0. 3 3 3 V
$$
E. $$
= 0. 5 1 0 V
$$
F. $$
= 0. 3 9 2 V
$$
G. $$
= 0. 4 5 6 V
$$
H. $$
= 0. 6 1 7 V
$$
I. $$
= 0. 5 0 3 V
$$
J. $$
= 0. 4 0 1 V
$$
Answer: A
A vertically polarized wave is incident on the water-air interface at a 45° angle from inside the water, where the parameters for water are $\mu = \mu_{0}$, $\varepsilon = 81 \varepsilon_{0}$, $\sigma = 0$. If at $t=0$, $z=0$, the electric field of the incident wave $E_{\mathrm{im}} = 1 \, \mathrm{V/m}$, find the value of the electric field in the air near the interface is().

Options:
A. $$
= 7 9. 0 \ ( \mu\mathrm{V / m} )
$$
B. $$
= 7 3. 6 \ ( \mu\mathrm{V / m} )
$$
C. $$
= 9 1. 4 \ ( \mu\mathrm{V / m} )
$$
D. $$
= 6 8. 9 \ ( \mu\mathrm{V / m} )
$$
E. $$
= 8 2. 1 \ ( \mu\mathrm{V / m} )
$$
F. $$
= 6 1. 8 \ ( \mu\mathrm{V / m} )
$$
G. $$
= 8 3. 7 \ ( \mu\mathrm{V / m} )
$$
H. $$
= 5 4. 3 \ ( \mu\mathrm{V / m} )
$$
I. $$
= 6 5. 2 \ ( \mu\mathrm{V / m} )
$$
J. $$
= 7 2. 5 \ ( \mu\mathrm{V / m} )
$$
Answer: B
The Magellanic Stream orbits the Milky Way and extends from 50 kpc to 100 kpc from the Galactic center.
Consider a clump of gas in the stream in a circular orbit about the Galactic center. Take the radius of the orbit to be 75 kpc and the orbital speed to be $2 4 4$ km $\mathrm{s}^{-1}$ . Treating the Galaxy and the mass clump as point masses, estimate the mass of the Milky Way. What is the corresponding mass-to-light ratio?

Options:
A. $$
M / L_{B}=3 8 \, \mathrm{M}_{\odot} / L_{\odot}
$$
B. $$
M / L_{B}=7 0 \, \mathrm{M}_{\odot} / L_{\odot}
$$
C. $$
M / L_{B}=5 5 \, \mathrm{M}_{\odot} / L_{\odot}
$$
D. $$
M / L_{B}=5 0 \, \mathrm{M}_{\odot} / L_{\odot}
$$
E. $$
M / L_{B}=4 0 \, \mathrm{M}_{\odot} / L_{\odot}
$$
F. $$
M / L_{B}=4 5 \, \mathrm{M}_{\odot} / L_{\odot}
$$
G. $$
M / L_{B}=6 5 \, \mathrm{M}_{\odot} / L_{\odot}
$$
H. $$
M / L_{B}=3 5 \, \mathrm{M}_{\odot} / L_{\odot}
$$
I. $$
M / L_{B}=6 0 \, \mathrm{M}_{\odot} / L_{\odot}
$$
J. $$
M / L_{B}=4 2 \, \mathrm{M}_{\odot} / L_{\odot}
$$
Answer: F
As the steeping time of the tea extends to approximately () minutes, the polyphenol compounds in the tea leaves are gradually extracted, resulting in an increase in bitterness and astringency of the tea infusion.

Options:
A. 5
B. 7
C. 3
D. 6
E. 9
F. 8
G. 20
H. 15
I. 12
J. 10
Answer: A
If the initial conditions for the Lagrangian gyro are $\theta=60^{\circ}, \ \dot{\theta}=0, \ \dot{\varphi}=2 \sqrt{\frac{m g l} {3 I_{1}}}, \ \omega_{z}=\frac{I_{1}} {I_{3}} \sqrt{\frac{3 m g l} {I_{1}}}$, determine the value of $\sec \theta=()$ in the subsequent motion.

Options:
A. $$
1+\cosh {\sqrt{\frac{3 m g l} {I_{1}}}} t
$$
B. $$
1-\operatorname{sech} {\sqrt{\frac{3 m g l} {I_{1}}}} t
$$
C. $$
1+\sin {\sqrt{\frac{3 m g l} {I_{1}}}} t
$$
D. $$
1+\operatorname{tanh} {\sqrt{\frac{m g l} {3 I_{1}}}} t
$$
E. $$
1+\operatorname{coth} {\sqrt{\frac{m g l} {I_{1}}}} t
$$
F. $$
1+\operatorname{s e c h} {\sqrt{\frac{m g l} {I_{1}}}} t
$$
G. $$
1-\sin {\sqrt{\frac{m g l} {I_{1}}}} t
$$
H. $$
1+\operatorname{csch} {\sqrt{\frac{3 m g l} {I_{1}}}} t
$$
I. $$
1-\operatorname{tanh} {\sqrt{\frac{m g l} {I_{1}}}} t
$$
J. $$
1-\cosh {\sqrt{\frac{m g l} {3 I_{1}}}} t
$$
Answer: F
A system of particles is composed of a particle with mass $4m$ located at the point $(a, -a, 0)$, a particle with mass $3m$ located at the point $(-a, a, 0)$, and a particle with mass $2m$ located at the point $(a, a, 0)$. What is the inertia tensor relative to the coordinate origin?

Options:
A. $$
\lambda_{1}=3,\lambda_{2}=16,\lambda_{3}=17
$$
B. $$
\lambda_{1}=4,\lambda_{2}=13,\lambda_{3}=17
$$
C. $$
\lambda_{1}=5,\lambda_{2}=13,\lambda_{3}=18
$$
D. $$
\lambda_{1}=4,\lambda_{2}=14,\lambda_{3}=18
$$
E. $$
\lambda_{1}=3,\lambda_{2}=15,\lambda_{3}=19
$$
F. $$
\lambda_{1}=5,\lambda_{2}=12,\lambda_{3}=18
$$
G. $$
\lambda_{1}=5,\lambda_{2}=15,\lambda_{3}=16
$$
H. $$
\lambda_{1}=7,\lambda_{2}=14,\lambda_{3}=15
$$
I. $$
\lambda_{1}=6,\lambda_{2}=13,\lambda_{3}=19
$$
J. $$
\lambda_{1}=6,\lambda_{2}=14,\lambda_{3}=17
$$
Answer: D
Assume there is a spaceship that achieves acceleration solely by emitting photons. When this spaceship accelerates from rest to $v=0.6c$, what fraction of its rest mass is it compared to its initial value?

Options:
A. $$
\frac{1}{5}
$$
B. $$
\frac{3}{4}
$$
C. $$
\frac{1}{3}
$$
D. $$
\frac{5}{6}
$$
E. $$
\frac{2}{3}
$$
F. $$
\frac{3}{5}
$$
G. $$
\frac{4}{5}
$$
H. $$
\frac{1}{2}
$$
I. $$
\frac{1}{4}
$$
J. $$
\frac{2}{5}
$$
Answer: H
A rectangular container has a length, width, and height of 2m, 0.7m, and 0.6m respectively, and contains water to a depth of 0.3m. If the container is subjected to horizontal acceleration along the lengthwise direction with an acceleration of $a = 3 \mathrm{m} / \mathrm{s}^{2}$, what is the force exerted by the water on each wall of the container?

Options:
A. $$
2.10\times10^{3}\:(\mathrm{N})
$$
B. $$
3.00\times10^{3}\:(\mathrm{N})
$$
C. $$
2.45\times10^{3}\:(\mathrm{N})
$$
D. $$
0.60\times10^{3}\:(\mathrm{N})
$$
E. $$
0.85\times10^{3}\:(\mathrm{N})
$$
F. $$
1.50\times10^{3}\:(\mathrm{N})
$$
G. $$
1.10\times10^{3}\:(\mathrm{N})
$$
H. $$
1.25\times10^{3}\:(\mathrm{N})
$$
I. $$
1.85\times10^{3}\:(\mathrm{N})
$$
J. $$
0.75\times10^{3}\:(\mathrm{N})
$$
Answer: H
The gravitational acceleration at location A is $979.442 \mathrm{cm/s^{2}}$, and at location B it is $980.129 \mathrm{cm/s^{2}}$. How many seconds does a pendulum clock that is set for location A gain or lose in 24 hours after being moved to location B, assuming other conditions remain unchanged?

Options:
A. Gains 15.00 seconds every 24 hours.
B. Loses 52.48 seconds every 24 hours.
C. Gains 5.40 seconds every 24 hours.
D. Loses 30.30 seconds every 24 hours.
E. Loses 28.52 seconds every 24 hours.
F. Gains 22.35 seconds every 24 hours.
G. Loses 15.67 seconds every 24 hours.
H. Gains 30.30 seconds every 24 hours.
I. Loses 10.00 seconds every 24 hours.
J. Gains 42.11 seconds every 24 hours.
Answer: H
A shunt-wound DC motor operates under the conditions of rated voltage $\mathbf{U}_{\mathrm{N}}=220 \mathbf{V}$ and rated current $\mathrm{I}_{\mathrm{N}}=80 \mathrm{A}$. The armature resistance at 75°C is $\mathbf{R}_{a}=0.01 \Omega$, the brush contact voltage drop is $2 \Delta\mathbf{U}_{\mathrm{b}}=2 \mathbf{V}$, and the total resistance in the excitation circuit is $\mathbf{R}_{\mathrm{rf}}+\mathbf{R}_{\mathrm{pf}}=110 \Omega$. The additional losses are $p_{s}=0.01 \mathrm{P}_{\mathrm{N}}$, and the efficiency is $\eta=0.85$. What is the armature copper loss $p_{cu a}$?

Options:
A. 68w
B. 45w
C. 74w
D. 82w
E. 50w
F. 55w
G. 72w
H. 90w
I. 60w
J. 61w
Answer: J
A separately excited DC motor has the following nameplate data: $\mathrm{P}_{\mathrm{N}}=7.5 \mathrm{kW}, \; \mathrm{U}_{\mathrm{N}}=220 \mathrm{V}, \; \mathrm{I}_{\mathrm{N}}=40.8 \mathrm{A}$, $\mathrm{n}_{\mathrm{N}}=1500 \, \mathrm{r} / \operatorname*{min}$, $\mathrm{R}_{\mathrm{a}}=0.36 \Omega$. Assuming the shaft load torque $\mathrm{T_{z}}=0.8 \mathrm{T_{N}}$, and other conditions remain unchanged, what is the speed of the motor when the magnetic flux decreases to $0.5 \phi_{\mathrm{N}}$?

Options:
A. 3042r/min
B. 1800r/min
C. 3600r/min
D. 3200r/min
E. 2900r/min
F. 2200r/min
G. 3000r/min
H. 1500r/min
I. 2500r/min
J. 2700r/min
Answer: A
Wound rotor induction motor $\mathrm{P_{N}=17\ kW, \ n_{N}=970\ r/min, \ \lambda_{M}=2.5, \ E_{2N}=230\ V, \ I_{2N}=33\ A}$: If the motor is required to achieve the shortest starting time, what resistance should be connected in series with the rotor circuit?

Options:
A. 0.19Ω
B. 0.28Ω
C. 0.10Ω
D. 0.12Ω
E. 0.35Ω
F. 0.25Ω
G. 0.22Ω
H. 0.15Ω
I. 0.40Ω
J. 0.30Ω
Answer: A
In a certain region, the initial temperature of the soil was 4°C. When a cold spell arrives, the surface temperature of the soil suddenly drops to -10°C, and it is assumed to remain at this temperature. Try to determine the time it takes for the temperature at a depth of 1 meter in the soil to drop to 0°C, and calculate the amount of heat conducted away from each square meter of the soil surface. Given that the thermal conductivity and thermal diffusivity of the soil are $k=0.5 \mathrm{W}/(\mathrm{m} \ \mathrm{K})$, and $\alpha=1.36 \times 10^{-7} \, \mathrm{m}^{2}/\mathrm{s}$, respectively.

Options:
A. $$
=-5. 0 1 \times1 0^{6} \ \mathrm{J / m}^{2}
$$
B. $$
=+3. 9 1 \times1 0^{7} \ \mathrm{J / m}^{2}
$$
C. $$
=+4. 0 5 \times1 0^{6} \ \mathrm{J / m}^{2}
$$
D. $$
=+6. 8 2 \times1 0^{6} \ \mathrm{J / m}^{2}
$$
E. $$
=-2. 7 9 \times1 0^{5} \ \mathrm{J / m}^{2}
$$
F. $$
=-4. 0 3 \times1 0^{7} \ \mathrm{J / m}^{2}
$$
G. $$
=+5. 0 2 \times1 0^{8} \ \mathrm{J / m}^{2}
$$
H. $$
=-3. 8 2 \times1 0^{7} \ \mathrm{J / m}^{2}
$$
I. $$
=-1. 8 2 \times1 0^{8} \ \mathrm{J / m}^{2}
$$
J. $$
=-7. 9 2 \times1 0^{7} \ \mathrm{J / m}^{2}
$$
Answer: H
The specific heat of water is known to be 4.18 joules/gram·kelvin.
If water at $0^{\circ} \ \mathrm{C}$ first comes into contact with a heat source at 50°C and reaches equilibrium, and then with a heat source at $100°C$ and reaches equilibrium, what is the change in entropy of the entire system?

Options:
A. $$ 9 0. 2 J/ka $$
B. $$ 9 3. 6 J/ka $$
C. $$ 9 4. 1 J/ka $$
D. $$ 9 5. 4 J/ka $$
E. $$ 9 0. 8 J/ka $$
F. $$ 9 2. 5 J/ka $$
G. $$ 9 1. 9 J/ka $$
H. $$ 9 6. 5 J/ka $$
I. $$ 9 8. 3 J/ka $$
J. $$
9 7. 2 J/ka
$$
Answer: J
Write the component matrices of the bivectors $\boldsymbol{e}_{3} \boldsymbol{e}_{1}$ and $\boldsymbol{e}_{1} \boldsymbol{e}_{3}$ in the Cartesian coordinate system.

Options:
A. $$
\left[ \begin{matrix} {{0}} & {{0}} & {{0}} \\ {{1}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{0}} \\ \end{matrix} \right]
$$
B. $$
\left[ \begin{matrix} {{1}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{0}} \\ \end{matrix} \right]
$$
C. $$
\left[ \begin{matrix} {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{0}} \\ {{0}} & {{1}} & {{0}} \\ \end{matrix} \right]
$$
D. $$
\left[ \begin{matrix} {{0}} & {{0}} & {{0}} \\ {{0}} & {{1}} & {{0}} \\ {{0}} & {{0}} & {{0}} \\ \end{matrix} \right]
$$
E. $$
\left[ \begin{matrix} {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ {{0}} & {{0}} & {{0}} \\ \end{matrix} \right]
$$
F. $$
\left[ \begin{matrix} {{0}} & {{1}} & {{1}} \\ {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{0}} \\ \end{matrix} \right]
$$
G. $$
\left[ \begin{matrix} {{0}} & {{1}} & {{0}} \\ {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{0}} \\ \end{matrix} \right]
$$
H. $$
\left[ \begin{matrix} {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right]
$$
I. $$
\left[ \begin{matrix} {{0}} & {{0}} & {{1}} \\ {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{0}} \\ \end{matrix} \right]
$$
J. $$
\left[ \begin{matrix} {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{0}} \\ {{1}} & {{0}} & {{0}} \\ \end{matrix} \right]
$$
Answer: I
Write the relationship between electromagnetic field strength and electromagnetic potential, as well as the general gauge transformation.

Options:
A. $$
\boldsymbol{B}=\boldsymbol{A}\cdot\nabla
$$
$$
E=-\nabla\varphi+\frac{\partial A} {\partial t}
$$
$$
\boldsymbol{A} \to\boldsymbol{A}^{\prime}=\boldsymbol{A}-\nabla\psi
$$
$$
\varphi\to\varphi^{\prime}=\varphi+\frac{\partial\psi} {\partial t}
$$
B. $$
\boldsymbol{B}=\nabla\cdot\boldsymbol{A}
$$
$$
E=\nabla\varphi-\frac{\partial A} {\partial t}
$$
$$
\boldsymbol{A} \to\boldsymbol{A}^{\prime}=\boldsymbol{A}+\psi
$$
$$
\varphi\to\varphi^{\prime}=\varphi+\frac{\partial\psi} {\partial t}
$$
C. $$
\boldsymbol{B}=\nabla\times\boldsymbol{A}
$$
$$
E=-\nabla\varphi-\frac{\partial A} {\partial t}
$$
$$
\boldsymbol{A} \to\boldsymbol{A}^{\prime}=\boldsymbol{A}+\nabla\psi
$$
$$
\varphi\to\varphi^{\prime}=\varphi-\frac{\partial\psi} {\partial t}
$$
D. $$
\boldsymbol{B}=\nabla\times\boldsymbol{A}
$$
$$
E=-\nabla\varphi-\frac{\partial A} {\partial t}
$$
$$
\boldsymbol{A} \to\boldsymbol{A}^{\prime}=\boldsymbol{A}+\nabla\psi
$$
$$
\varphi\to\varphi^{\prime}=\varphi+\frac{\partial\psi} {\partial t}
$$
E. $$
\boldsymbol{B}=\nabla+\boldsymbol{A}
$$
$$
E=\nabla\varphi+\frac{\partial A} {\partial t}
$$
$$
\boldsymbol{A} \to\boldsymbol{A}^{\prime}=\boldsymbol{A}+\nabla\phi
$$
$$
\varphi\to\varphi^{\prime}=\varphi-\frac{\partial\phi} {\partial t}
$$
F. $$
\boldsymbol{B}=\nabla\times\boldsymbol{A}
$$
$$
E=-\nabla\varphi+\frac{\partial A} {\partial t}
$$
$$
\boldsymbol{A} \to\boldsymbol{A}^{\prime}=\boldsymbol{A}+\nabla\phi
$$
$$
\varphi\to\varphi^{\prime}=\varphi+\frac{\partial\phi} {\partial t}
$$
G. $$
\boldsymbol{B}=\nabla\times\boldsymbol{A}
$$
$$
E=\nabla\varphi+\frac{\partial A} {\partial t}
$$
$$
\boldsymbol{A} \to\boldsymbol{A}^{\prime}=\boldsymbol{A}+\nabla\phi
$$
$$
\varphi\to\varphi^{\prime}=\varphi-\frac{\partial\phi} {\partial t}
$$
H. $$
\boldsymbol{B}=\nabla\cross\boldsymbol{A}
$$
$$
E=\nabla\varphi-\frac{\partial A} {\partial t}
$$
$$
\boldsymbol{A} \to\boldsymbol{A}^{\prime}=\boldsymbol{A}-\nabla\psi
$$
$$
\varphi\to\varphi^{\prime}=\varphi+\frac{\partial\psi} {\partial t}
$$
I. $$
\boldsymbol{B}=\nabla+\boldsymbol{A}
$$
$$
E=-\nabla\varphi+\frac{\partial A} {\partial t}
$$
$$
\boldsymbol{A} \to\boldsymbol{A}^{\prime}=\boldsymbol{A}-\nabla\phi
$$
$$
\varphi\to\varphi^{\prime}=\varphi+\frac{\partial\phi} {\partial t}
$$
J. $$
\boldsymbol{B}=\nabla\boldsymbol{A}
$$
$$
E=-\nabla\varphi-\frac{\partial A} {\partial t}
$$
$$
\boldsymbol{A} \to\boldsymbol{A}^{\prime}=\boldsymbol{A}-\nabla\psi
$$
$$
\varphi\to\varphi^{\prime}=\varphi+\frac{\partial\psi} {\partial t}
$$
Answer: C
The method for the development and research of item group training is ().

Options:
A. Continuous Running Strategy
B. Interval Training Method
C. Randomized Motion Plan
D. Gradual Overload Design
E. Repetition Practice Model
F. Resistance-Based Training
G. Circuit Training Technique
H. Sprint-Focused System
I. Pyramid Intensity Approach
J. Split Test Progression
Answer: B
Assume that all of the ions escaping Io are sulfur ions. Assuming also that this rate has been constant over the last 4.55 billion years, estimate the amount of mass lost from the moon since its formation. Compare your answer with Io's present mass $( 8. 9 3 2 \times1 0^{2 2} \ \mathrm{k g}$ ).

Options:
A. 1.93%
B. 3.62%
C. 0.85%
D. 7.29%
E. 5.87%
F. 2.48%
G. 9.54%
H. 6.14%
I. 8.31%
J. 4.76%
Answer: C
A straight line charge with a length of $2l$ and a linear charge density of $\tau$. Find the electric field intensity and potential at a point on the perpendicular bisector of the line charge, located at a distance $2l$ from the center of the line charge is ().

Options:
A. $$
\frac{\tau l^{2}} {2 {\pi} \varepsilon_{0} {\sqrt{3}}}
$$
$$
\frac{0. 1 8 \tau} {2 \pi\varepsilon_{0}}
$$
B. $$
\frac{\tau l} {3 {\sqrt{10}} \varepsilon_{0} \pi}
$$
$$
\frac{0. 4 0 \tau} {4 \pi\varepsilon_{0}}
$$
C. $$
\frac{\tau l} {{\sqrt{6}} 2 \pi\varepsilon_{0}}
$$
$$
\frac{0. 1 2 \tau} {3 \pi\varepsilon_{0}}
$$
D. $$
\frac{2 \tau} {{\sqrt{7}} \pi\varepsilon_{0} l}
$$
$$
\frac{0. 3 6 \tau} {4 \pi\varepsilon_{0}}
$$
E. $$
\frac{\tau} {{\sqrt{2}} \pi\varepsilon_{0} l^{2}}
$$
$$
\frac{0. 4 2 \tau} {3 \pi\varepsilon_{0}}
$$
F. $$
\frac{4 \tau} {\pi \varepsilon_{0} l {\sqrt{9}}}
$$
$$
\frac{0. 3 0 \tau} {5 \pi\varepsilon_{0}}
$$
G. $$
\frac{\pi e_{x}} {4 {\sqrt{5}} \pi\varepsilon_{0} l}
$$
$$
\frac{0. 2 4 \tau} {\pi\varepsilon_{0}}
$$
H. $$
\frac{\tau} {6 {\sqrt{5}} \varepsilon_{0} l \pi}
$$
$$
\frac{0. 4 8 \tau} {2 \pi\varepsilon_{0}}
$$
I. $$
\frac{\tau} {\pi\varepsilon_{0} {\sqrt{4}} l^{2}}
$$
$$
\frac{0. 2 9 \tau} {3 \pi\varepsilon_{0}}
$$
J. $$
\frac{\tau l^{3}} {4 \pi\varepsilon_{0} {\sqrt{8}}}
$$
$$
\frac{0. 2 2 \tau} {6 \pi\varepsilon_{0}}
$$
Answer: G
Let the reference point for the vector potential be at infinity. The vector potential generated on the axis of a circular loop of wire with radius $R$, carrying a current $I$ is ().

Options:
A. $$
A={\frac{\mu_{0} I} {4 \pi z^{2}}} \oint_{l} \mathrm{d} I=0
$$
B. $$
A={\frac{\mu_{0} I} {4 \pi{\sqrt{z^{2}+R^{2}}}}} \oint_{l} \mathrm{d} I=0
$$
C. $$
A={\frac{\mu_{0} I z} {4 \pi R^{2}}} \oint_{l} \mathrm{d} I=0
$$
D. $$
A={\frac{\mu_{0} I (z^{2}+R)} {4 \pi{\sqrt{z^{2}+R^{2}}}}} \oint_{l} \mathrm{d} I=0
$$
E. $$
A={\frac{\mu_{0} I} {8 \pi \sqrt{z^{2}+R^{2}}}} \oint_{l} \mathrm{d} I=0
$$
F. $$
A={\frac{\mu_{0} I R} {8 \pi (z^{2}+1)}} \oint_{l} \mathrm{d} I=0
$$
G. $$
A={\frac{\mu_{0} I R^2} {4 \pi (z^{2}+R^{2})^{3/2}}} \oint_{l} \mathrm{d} I=0
$$
H. $$
A={\frac{\mu_{0} I z} {4 \pi{\sqrt{z^{2}+R^{2}}}}} \oint_{l} \mathrm{d} I=0
$$
I. $$
A={\frac{\mu_{0} I} {2 \pi{\sqrt{z^{2}+R^{2}}}}} \oint_{l} \mathrm{d} I
$$
J. $$
A={\frac{\mu_{0} I R} {4 \pi (z^{2}+R^{2})}} \oint_{l} \mathrm{d} I=0
$$
Answer: B
A rectangular conductor frame with a width of $a$ and a length of $b$ is placed in a magnetic field, where the magnetic flux density is $B = B_0 \sin \omega t \, e_y$. When the conductor frame is stationary, its normal direction $e_n$ forms an angle of $\alpha$ with $e_y$. What is the induced electromotive force when the conductor frame is stationary or rotating around the $x$-axis at an angular velocity of $o$ (assuming that at time $t = 0$, $\alpha = 0$)?

Options:
A. $$
- a b B_{0} \sin 2 \omega t
$$
B. $$
a b B_{0} \sin \omega t
$$
C. $$
a b \omega B_{0} \sin \alpha
$$
D. $$
a b \omega B_{0}\operatorname{c o s} \omega t
$$
E. $$
a b B_{0} \operatorname{c o s} \omega t
$$
F. $$
a b B_{0}\operatorname{c o s} \alpha
$$
G. $$
- a B_{0} \omega \sin 2 \omega t
$$
H. $$
- a b B_{0} \omega\operatorname{c o s} 2 \omega t
$$
I. $$
- a b \alpha B_{0}\operatorname{c o s} \omega t
$$
J. $$
- b B_{0} \omega\operatorname{c o s} \omega t
$$
Answer: H
A capacitor with an air dielectric, if the voltage between the plates remains unchanged, is filled with oil with a dielectric constant of $\varepsilon=4 \varepsilon_{0}$ between the plates. If the charge remains unchanged, what are the energy densities in the capacitor before and after the oil is filled?

Options:
A. $0.25w_0,4w_0$
B. $w_0,4w_0$
C. $6w_0,0.25w_0$
D. $2w_0,0.5w_0$
E. $4w_0,0.2w_0$
F. $4w_0,2w_0$
G. $3w_0,0.33w_0$
H. $5w_0,0.5w_0$
I. $4w_0,0.75w_0$
J. $4w_0,0.25w_0$
Answer: J
A uniform plane wave with a frequency of $f = 300 \ \mathrm{MHz}$ obliquely incident from medium $1 \, (\boldsymbol{\mu}_{1} = \boldsymbol{\mu}_{0}, \, \boldsymbol{\varepsilon}_{1} = 4 \boldsymbol{\varepsilon}_{0}, \, \boldsymbol{\sigma}_{1} = 0)$ onto medium $2 \, (\mu_{2} = \mu_{0}, \, \varepsilon_{2} = \varepsilon_{0}, \, \sigma_{2} = 0)$. If the incident wave is a vertically polarized wave and the angle of incidence $\theta_{1} = 60^\circ$, what is the propagation direction of the transmitted wave in air? What is its phase velocity?

Options:
A. $$
= 1. 7 5 \times1 0^{8} \mathrm{\ m / s}
$$
B. $$
= 1. 6 7 \times1 0^{8} \mathrm{\ m / s}
$$
C. $$
= 2. 1 6 \times1 0^{8} \mathrm{\ m / s}
$$
D. $$
= 1. 9 2 \times1 0^{8} \mathrm{\ m / s}
$$
E. $$
= 2. 3 1 \times1 0^{8} \mathrm{\ m / s}
$$
F. $$
= 1. 4 9 \times1 0^{8} \mathrm{\ m / s}
$$
G. $$
= 2. 0 2 \times1 0^{8} \mathrm{\ m / s}
$$
H. $$
= 1. 8 4 \times1 0^{8} \mathrm{\ m / s}
$$
I. $$
= 1. 7 3 \times1 0^{8} \mathrm{\ m / s}
$$
J. $$
= 1. 5 6 \times1 0^{8} \mathrm{\ m / s}
$$
Answer: I