MikaStars39/nano-eval huggingface dataset:
Set
$$
\mathrm{X_{1}, ~ X_{2}, ~..., ~ X_{n} ~ ( n \geq2 ) ~}
$$
be a simple random sample from a population
$$
\mathrm{N} \ ( \mu, \ \sigma^{2} ) \ \ ( \sigma> 0 )
$$
Set
$$
\overline{{{{X}}}}=\frac{1} {n} \sum_{i=1}^{n} X_{i}
$$
$$
S={\sqrt{{\frac{1} {n-1}} \sum_{i=1}^{n} \left( X_{i}-{\overline{{{X}}}} \right)^{2}}}
$$
$$
S^{*}=\sqrt{\frac{1} {n} \sum_{i=1}^{n} \bigl( X_{i}-\mu\bigr)^{2}}
$$
So then()

Options:
A. $$
\begin{array} {l} {{{{\mathrm{}} \; \; \frac{\sqrt{n} \left( \bar{X}-\mu\right)} {S^{*}}-t \left( n \right)}}}
\end{array}
$$
B. $$\mathrm{} \ \frac{\sqrt{n} \left( \bar{X}-\mu\right)} {S^{*}} \sim t(n-2)$$
C. $$\mathrm{} \ \frac{\sqrt{n} \left( \bar{X}-\mu\right)} {S^{*}} \sim N(0, 1)$$
D. $$\mathrm{} \ \frac{\sqrt{n} \left( \bar{X}-\mu\right)} {\sigma} \sim N(0, 1)$$
E. $$
\begin{array} {l} {{{{\mathrm{}} \; \; \frac{\sqrt{n} \left( \bar{X}-\mu\right)} {S^{*}}-t \left( n -1\right)}}}
\end{array}
$$
F. $$
\mathrm{} \ \frac{\sqrt{n} \left( \bar{X}-\mu\right)} {S} \sim t \left( n \right)
$$
G. $$\mathrm{} \ \frac{\sqrt{n-1} \left( \bar{X}-\mu\right)} {S} \sim t(n-1)$$
H. $$\mathrm{} \ \frac{\sqrt{n+1} \left( \bar{X}-\mu\right)} {S} \sim t(n+1)$$
I. $$
\mathrm{} \ \ {\frac{{\sqrt{n}} \left( {\bar{X}}-\mu\right)} {S}}-t \left( n {-} 1 \right)
$$
J. $$\mathrm{} \ \frac{\sqrt{n-1} \left( \bar{X}-\mu\right)} {S^{*}} \sim t(n)$$
Answer: I
Let $x_1, x_2, ..., x_n$ ($n > 2$) be a sample from population X, and let $E(X) = \mu$ (where $\mu$ is unknown), with x represents the sample mean.The unbiased estimate of $\mu$ is $\ ( \qquad\mathrm{~ ) ~}$.

Options:
A. $n{\bar x}$
B. ${\bar x}/(n-1)$
C. $(x_1 + x_2 + \ldots + x_n)/n$
D. $\frac{1}{n}(x_1 + x_2 + \ldots + x_n)$
E. $\sqrt{{\bar x}}$
F. ${\bar x}$
G. $n(x_1 + x_2 + \ldots + x_n)/n$
H. $(n-1){\bar x}$
I. ${\bar x}^2$
J. $(x_1 + x_2...+x_n)$
Answer: F
Draw parallel chords in a circle of radius R. If the points of intersection of these chords with a diameter perpendicular to the chords are equidistant on the diameter, then the probability that the intersection point lies within a line segment on the diameter is proportional to the length of the line segment. What is the probability that any randomly drawn chord is longer than R?

Options:
A. $P(A)=0.367$
B. $P(A)=0.397$
C. $P(A)=0.724$
D. $P(A)=0.957$
E. $P(A)=0.492$
F. $P(A)=0.866$
G. $P(A)=0.347$
H. $P(A)=0.625$
I. $P(A)=0.357$
J. $P(A)=0.377$
Answer: F
Given that the random variable X has the density function:
$$
p ( x )=\left\{\begin{matrix} {{{x,}}} & {{{-1 \leq x \leq1}}} \\{{{2-x,}}} & {{{1 \leq x <2}}}\\ {{{0,}}} & {{{others}}} \\ \end{matrix} \right.
$$
What is the probability of $P(X \le 1.5)=$_______?.

Options:
A. 0.950
B. 0.825
C. 0.875
D. 0.925
E. 0.975
F. 0.700
G. 0.750
H. 0.900
I. 0.650
J. 0.800
Answer: C
After a bulldozer in a certain factory breaks down, the repair time T is a random variable (unit: hours), and its density function is
$$
p ( t )=\left\{\begin{aligned} {{0. 0 2 e^{-0. 0 2 t},}} & {{{} t > 0}} \\ {{0,}} & {{{} t \leq0}} \\ \end{aligned} \right.
$$
The average maintenance time is ____.

Options:
A. $E(T)=55$
B. $E(T)=100$
C. $E(T)=50$
D. $E(T)=40$
E. $E(T)=25$
F. $E(T)=30$
G. $E(T)=45$
H. $E(T)=75$
I. $E(T)=60$
J. $E(T)=65$
Answer: C
Select a point randomly in the interval (0,1) and denote it as X.
$\mathrm{P} \ \ ( \mathrm{X}^{2} \!-\! 3 \mathrm{X} / 4 \!+\! 1 / 8 \! \geq\! 0 )$ is ____.

Options:
A. 0.60
B. 0.75
C. 0.50
D. 0.20
E. 0.95
F. 0.40
G. 0.30
H. 0.25
I. 1.00
J. 0.85
Answer: B
What are the values of the following limits?$$ \operatorname* {l i m}_{n \to\infty} \sum_{k=1}^{n} {\frac{k} {n^{2}}} \operatorname{l n} ( 1+{\frac{k} {n}} ) $$

Options:
A. $$
{\frac{1} {4}} \operatorname{l n} 4
$$
B. $$
{\frac{1} {8}} \operatorname{l n} 8
$$
C. $$
\operatorname{l n} ( 4 )
$$
D. $$
{\frac{1} {2}}
$$
E. $$
{\frac{1} {8}}
$$
F. $$
{\frac{1} {2}} \operatorname{l n} 2
$$
G. $$
{\frac{1} {2}} \operatorname{l n} 4
$$
H. $$
{\frac{1} {4}}
$$
I. $$
\operatorname{l n} ( 2 )
$$
J. $$
\operatorname{l n} ( 8 )
$$
Answer: H
Given that the function expression is $f \left( x, y \right)=\begin{cases} {{x y, x y=0}} \\ {{x, y=0}} \\ {{y, x=0}} \\ \end{cases}$ , what are the solutions of the following four expressions ${\partial} {\mathrm{f}} / {\partial } \textbf{x} |_{( 0, \ 0 )}$, $\partial^{2} {\bf f}/\partial{\bf x} \partial{\bf y} |_{( 0, \ 0 )}$, $\operatorname* {l i m}_{( x, y ) \to( 0, 0 )} f \left( x, y \right)$, and $\operatorname* {l i m}_{( x, y ) \to( 0, 0 )} f \left( x, y \right)$?

Options:
A. $$
1 \,, \; inexistence \; \,, \; \; 0 \,, \; \; 0
$$
B. $$
1 \,, \; 1 \; \,, \; \; 1\,, \; \; inexistence
$$
C. $$
1 \,, \; 1 \; \,, \; \; inexistence \,, \; \; 1
$$
D. $$
0 \,, \; inexistence \; \,, \; \; 0 \,, \; \; 1
$$
E. $$
0 \,, \; 0 \; \,, \; \; 0 \,, \; \; inexistence
$$
F. $$
0 \,, \; 0 \; \,, \; \; inexistence \,, \; \; 0
$$
G. $$
inexistence \,, \; 0 \; \,, \; \; 0 \,, \; \; 1
$$
H. $$
0 \,, \; 0 \; \,, \; \; 1 \,, \; \; 1
$$
I. $$
1 \,, \; 1\; \,, \; \; 0 \,, \; \; 0
$$
J. $$
inexistence \,, \; 1 \; \,, \; \; 1 \,, \; \; 1
$$
Answer: A
Let $\Sigma$ be the lower side of the surface $z={\sqrt{x^{2}+y^{2}}} ( 1 \leq x^{2}+y^{2} \leq4 )$ and $\mathbf{f} \ ( \mathbf{x} )$ be a continuous function, then what is the value of $I=\operatorname* \iint _{\Sigma } \left[ x f ( x y )+2 x y-y \right] {\mathrm{d y d}} z+\left[ y f ( x y )+2 y+x \right] {\mathrm{d}} z {\mathrm{d}} x+\left[ z f ( x y )+z \right] {\mathrm{d}} x {\mathrm{d}} y$?

Options:
A. $$
16 \pi
$$
B. $$
{\frac{1} {2}} \pi
$$
C. $$
{\frac{3} {4}} \pi
$$
D. $$
5 \pi
$$
E. $$
0
$$
F. $$
2 \pi
$$
G. $$
3 \pi
$$
H. $$
{\frac{1} {4}} \pi
$$
I. $$
{\frac{1} {8}} \pi
$$
J. $$
8 \pi
$$
Answer: E
What is the rank of the following matrix?
$$A=\left( \begin{matrix} {{{{3}}}} & {{{{2}}}} & {{{{-1}}}} & {{{{-3}}}} & {{{{-1}}}} \\ {{{{2}}}} & {{{{-1}}}} & {{{{3}}}} & {{{{1}}}} & {{{{-3}}}} \\ {{{{7}}}} & {{{{0}}}} & {{{{5}}}} & {{{{-1}}}} & {{{{-8}}}} \\ \end{matrix} \right)$$

Options:
A. $$
R ( A )=7
$$
B. $$
R ( A )=10
$$
C. $$
R ( A )=3
$$
D. $$
R ( A )=4
$$
E. $$
R ( A )=8
$$
F. $$
R ( A )=1
$$
G. $$
R ( A )=5
$$
H. $$
R ( A )=2
$$
I. $$
R ( A )=9
$$
J. $$
R ( A )=6
$$
Answer: C
Suppose the rank of $\left( \begin{matrix} {{{a}}} \\ {{{3}}} \\ {{{1}}} \\ \end{matrix} \right), \left( \begin{matrix} {{{2}}} \\ {{{b}}} \\ {{{3}}} \\ \end{matrix} \right), \left( \begin{matrix} {{{1}}} \\ {{{2}}} \\ {{{1}}} \\ \end{matrix} \right), \left( \begin{matrix} {{{2}}} \\ {{{3}}} \\ {{{1}}} \\ \end{matrix} \right)$ is 2, then what are the values of $a, b$ ?

Options:
A. $a=2$,$b=1$
B. $a=2$,$b=4$
C. $a=5$,$b=5$
D. $a=3$,$b=2$
E. $a=3$,$b=1$
F. $a=4$,$b=4$
G. $a=1$,$b=3$
H. $a=2$,$b=5$
I. $a=2$,$b=3$
J. $a=2$,$b=2$
Answer: H
What are the coordinates of the intersection of line ${\frac{x-1} {3}}={\frac{y+1} {-4}}={\frac{z+2} {-2}}$ and plane $4 x+5 y-3 z-7=0$ ?

Options:
A. $$
(1, 3, 0 )
$$
B. $$
(2, 1, 0 )
$$
C. $$
(-2, 3, 0 )
$$
D. $$
(-2, 3, 1 )
$$
E. $$
(-2, 3, 2 )
$$
F. $$
(-2, 3, -1 )
$$
G. $$
(1, 3, 3 )
$$
H. $$
(2, 3, 0 )
$$
I. $$
(1, 3, -2 )
$$
J. $$
(2, 2, 0 )
$$
Answer: C
Given that vector $\alpha=\left( \begin{matrix} {{{1}}} \\ {{{k}}} \\ {{{1}}} \\ \end{matrix} \right)$ is the eigenvector of the inverse matrix of $A=\left( \begin{matrix} {{2}} & {{1}} & {{1}} \\ {{1}} & {{2}} & {{1}} \\ {{1}} & {{1}} & {{2}} \\ \end{matrix} \right)$ , what is the value of $k$?

Options:
A. $$k=4
$$
B. $$k=2
$$
C. $$k=-4
$$
D. $$k=1
$$
E. $$k=3
$$
F. $$k=-3
$$
G. $$k=-2
$$
H. $$k=5
$$
I. $$k=-1
$$
J. $$k=0
$$
Answer: D
What is the inverse ordinal of permutation $1 \; ( k+1 ) \; 2 \; ( k+2 ) \; \cdots\; ( k-1 ) \; ( 2 k-1 ) \; k \; ( 2 k )$ ?

Options:
A. $$
\frac{1} {2} k ( k-1 )
$$
B. $$
\frac{1} {2} k ( k+1 )
$$
C. $$
\frac{1} {4} k ( k-1 )
$$
D. $$
\frac{1} {4} k ( k+1 )
$$
E. $$
\frac{1} {4} k ( k-2 )
$$
F. $$
\frac{1} {8} k ( k+1 )
$$
G. $$
\frac{1} {2} k ( k-2 )
$$
H. $$
\frac{1} {8} k ( k-1 )
$$
I. $$
\frac{3} {8} k ( k+1 )
$$
J. $$
\frac{3} {8} k ( k-1 )
$$
Answer: A
What is the result of using the Vandermond determinant?
$\left| \begin{matrix} {{1}} & {{1}} & {{\cdots}} & {{1}} \\ {{2}} & {{2^{2}}} & {{\cdots}} & {{2^{n}}} \\ {{3}} & {{3^{2}}} & {{\cdots}} & {{3^{n}}} \\ {{\cdots}} & {{\cdots}} & {{\cdots}} & {{\cdots}} \\ {{n}} & {{n^{2}}} & {{\cdots}} & {{n^{n}}} \\ \end{matrix} \right|$

Options:
A. $$
\prod_{i=1}^{n+4} i!
$$
B. $$
\prod_{i=1}^{n-2} i!
$$
C. $$
\prod_{i=1}^{n-3} i!
$$
D. $$
\prod_{i=1}^{n+3} i!
$$
E. $$
\prod_{i=1}^{n+5} i!
$$
F. $$
\prod_{i=1}^{n} i!
$$
G. $$
\prod_{i=1}^{n-1} i!
$$
H. $$
\prod_{i=1}^{n+1} i!
$$
I. $$
\prod_{i=1}^{n+2} i!
$$
J. $$
\prod_{i=1}^{n-4} i!
$$
Answer: F
What are the eigenroots of the following matrices?
$$
\left( \begin{matrix} {{{1}}} & {{{-2}}} & {{{2}}} \\ {{{-2}}} & {{{-2}}} & {{{4}}} \\ {{{2}}} & {{{4}}} & {{{-2}}} \\ \end{matrix} \right)
$$

Options:
A. $$
\lambda_{1}=-1 \;, \lambda_{2}=-1,\lambda_{3}=2
$$
B. $$
\lambda_{1}=-1 \;, \lambda_{2}=1,\lambda_{3}=2
$$
C. $$
\lambda_{1}=-4 \;, \lambda_{2}=\lambda_{3}=2
$$
D. $$
\lambda_{1}=-7 \;, \lambda_{2}=\lambda_{3}=1
$$
E. $$
\lambda_{1}=-1 \;, \lambda_{2}=\lambda_{3}=2
$$
F. $$
\lambda_{1}=-7 \;, \lambda_{2}=1,\lambda_{3}=2
$$
G. $$
\lambda_{1}=-1 \;, \lambda_{2}=1,\lambda_{3}=3
$$
H. $$
\lambda_{1}=-7 \;, \lambda_{2}=\lambda_{3}=2
$$
I. $$
\lambda_{1}=-1 \;, \lambda_{2}=0,\lambda_{3}=-2
$$
J. $$
\lambda_{1}=-1 \;, \lambda_{2}=1,\lambda_{3}=0
$$
Answer: H
What are the quotient and remainder of dividing $g (x)$ by $f (x)$ ?
$$
\quad f ( x )=x^{4}-2 \, x^{3}+x-1, g ( x )=3 x^{2}+x+1
$$

Options:
A. $$\frac{1} {9} x^{2}-\frac{7} {9} x+\frac{4} {2 7} \ \ \ \ \ \ \ \frac{4 4} {2 7} x-\frac{3 1} {2 7}$$
B. $$\frac{1} {6} x^{2}-\frac{7} {9} x+\frac{4} {2 7} \ \ \ \ \ \ \ \frac{4 4} {2 7} x-\frac{3 1} {2 7}$$
C. $$\frac{1} {8} x^{2}-\frac{7} {9} x+\frac{4} {2 7} \ \ \ \ \ \ \ \frac{4 4} {2 7} x-\frac{3 1} {2 7}$$
D. $$\frac{1} {3} x^{2}-\frac{11} {9} x+\frac{4} {2 7} \ \ \ \ \ \ \ \frac{4 4} {2 7} x-\frac{3 1} {2 7}$$
E. $$\frac{1} {2} x^{2}-\frac{7} {9} x+\frac{4} {2 7} \ \ \ \ \ \ \ \frac{4 4} {2 7} x-\frac{3 1} {2 7}$$
F. $$\frac{1} {7} x^{2}-\frac{7} {9} x+\frac{4} {2 7} \ \ \ \ \ \ \ \frac{4 4} {2 7} x-\frac{3 1} {2 7}$$
G. $$\frac{1} {3} x^{2}-\frac{5} {9} x+\frac{4} {2 7} \ \ \ \ \ \ \ \frac{4 4} {2 7} x-\frac{3 1} {2 7}$$
H. $$\frac{1} {3} x^{2}-\frac{7} {9} x+\frac{4} {2 7} \ \ \ \ \ \ \ \frac{4 4} {2 7} x-\frac{3 1} {2 7}$$
I. $$\frac{1} {4} x^{2}-\frac{7} {9} x+\frac{4} {2 7} \ \ \ \ \ \ \ \frac{4 4} {2 7} x-\frac{3 1} {2 7}$$
J. $$\frac{1} {5} x^{2}-\frac{7} {9} x+\frac{4} {2 7} \ \ \ \ \ \ \ \frac{4 4} {2 7} x-\frac{3 1} {2 7}$$
Answer: H
What is the invariant of X-square $\left( \begin{matrix} {{{x}}} & {{{{-1}}}} & {{{{1}}}} \\ {{{{-3}}}} & {{{{x+2}}}} & {{{{0}}}} \\ {{{{1}}}} & {{{{-1}}}} & {{{{x+1}}}} \\ \end{matrix} \right)$ of third order?

Options:
A. $$
d_{1} ( x )=d_{2} ( x )=2, d_{3} ( x )=( x-1 ) ( x^{2}+4 x+2 )
$$
B. $$
d_{1} ( x )=d_{2} ( x )=1, d_{3} ( x )=( x-1 ) ( x^{2}+4 x+1 )
$$
C. $$
d_{1} ( x )=d_{2} ( x )=5, d_{3} ( x )=( x-1 ) ( x^{2}+4 x+2 )
$$
D. $$
d_{1} ( x )=d_{2} ( x )=1, d_{3} ( x )=( x-1 ) ( x^{2}+4 x+2 )
$$
E. $$
d_{1} ( x )=d_{2} ( x )=0, d_{3} ( x )=( x-1 ) ( x^{2}+4 x+2 )
$$
F. $$
d_{1} ( x )=d_{2} ( x )=1, d_{3} ( x )=( x-1 ) ( x^{3}+4 x+2 )
$$
G. $$
d_{1} ( x )=d_{2} ( x )=6, d_{3} ( x )=( x-1 ) ( x^{2}+4 x+2 )
$$
H. $$
d_{1} ( x )=d_{2} ( x )=1, d_{3} ( x )=( x-2 ) ( x^{2}+4 x+2 )
$$
I. $$
d_{1} ( x )=d_{2} ( x )=4, d_{3} ( x )=( x-1 ) ( x^{2}+4 x+2 )
$$
J. $$
d_{1} ( x )=d_{2} ( x )=3, d_{3} ( x )=( x-1 ) ( x^{2}+4 x+2 )
$$
Answer: D
Let $R^{3}$have a linear transformation $\sigma$is defined as follows:$\sigma( x_{1}, x_{2}, x_{3} ) \! = \! ( x_{1}+x_{2}, \ x_{2}+x_{3}, \ x_{3} ), \ \ \forall( x_{1}, x_{2}, x_{3} ) \! \in\! R^{3}.$
Which of the following subspaces of $R^{3}$do not change under $\sigma$?
(1) $\{( 0, 0, c ) | \, c \! \in\! R \}$ ; (2) $\{( 0, b, c ) | \, b, c \! \in\! R \}$ ;
(3) $\{( a, 0, 0 ) | \, a \in R \}$ ; (4) $\{( a, b, 0 ) | \, a, b \in R \}$ ;
(5) $\{( a, 0, c ) | \, a, c \in R \}$ ; (6) $\{( a, \ -a, 0 ) | \ a \in R \}$

Options:
A. $$
( 3 ) , ( 4 )
$$
B. $$
( 1 ) , ( 2 )
$$
C. $$
( 1 ) , ( 3 )
$$
D. $$
( 5 ) , ( 6 )
$$
E. $$
( 1 ) , ( 5 )
$$
F. $$
( 4 ) , ( 6 )
$$
G. $$
( 3 ) , ( 5 )
$$
H. $$
( 2 ) , ( 4 )
$$
I. $$
( 3 ) , ( 6 )
$$
J. $$
( 2 ) , ( 6 )
$$
Answer: A
Transform the following quadratic form into its standard form using the method of completing the square. What is the result?
$$
f ( x_{1}, x_{2}, x_{3} )=x_{1}^{2}-3 x_{2}+4 x_{3}-2 x_{1} x_{2}+2 x_{1} x_{3}-1 0 x_{2} x_{3}
$$

Options:
A. $$
f=-w_{1}^{2}-4 w_{2}^{2}+7 w_{3}^{2}
$$
B. $$
f=w_{1}^{2}-4 w_{2}^{2}+7 w_{3}^{2}
$$
C. $$
f=w_{1}^{2}-4 w_{2}^{2}+6 w_{3}^{2}
$$
D. $$
f=3w_{1}^{2}-4 w_{2}^{2}+7 w_{3}^{2}
$$
E. $$
f=w_{1}^{2}-4 w_{2}^{2}-7 w_{3}^{2}
$$
F. $$
f=w_{1}^{2}-4 w_{2}^{2}+ w_{3}^{2}
$$
G. $$
f=2w_{1}^{2}-4 w_{2}^{2}+7 w_{3}^{2}
$$
H. $$
f=w_{1}^{2}+4 w_{2}^{2}+7 w_{3}^{2}
$$
I. $$
f=-3w_{1}^{2}-4 w_{2}^{2}+7 w_{3}^{2}
$$
J. $$
f=-2w_{1}^{2}-4 w_{2}^{2}+7 w_{3}^{2}
$$
Answer: B
Setting $A=\left( \begin{matrix} {{{1}}} & {{{1}}} & {{{a}}} \\ {{{1}}} & {{{a}}} & {{{1}}} \\ {{{a}}} & {{{1}}} & {{{1}}} \\ \end{matrix} \right), \beta=\left( \begin{matrix} {{{1}}} \\ {{{1}}} \\ {{{-2}}} \\ \end{matrix} \right)$ . It is known that the linear equation system $AX = \beta$ has infinitely many solutions. Can the value of $a$ be determined?

Options:
A. $$
a=-4
$$
B. $$
a=0
$$
C. $$
a=4
$$
D. $$
a=-1
$$
E. $$
a=-5
$$
F. $$
a=2
$$
G. $$
a=1
$$
H. $$
a=3
$$
I. $$
a=-3
$$
J. $$
a=-2
$$
Answer: J
Set matrix$A=\left( \begin{matrix} {{{1}}} & {{{-1}}} & {{{1}}} \\ {{{a}}} & {{{4}}} & {{{b}}} \\ {{{-3}}} & {{{-3}}} & {{{5}}} \\ \end{matrix} \right)$, given that $A$ has three linearly independent eigenvectors, $\lambda=2$ is the double eigenroot of $A$.
What is the value of $a$, $b$?

Options:
A. $$
a=-3, b=-2
$$
B. $$
a=1, b=-2
$$
C. $$
a=3, b=-2
$$
D. $$
a=2, b=0
$$
E. $$
a=-2, b=-2
$$
F. $$
a=2, b=-1
$$
G. $$
a=2, b=2
$$
H. $$
a=2, b=-5
$$
I. $$
a=0, b=-2
$$
J. $$
a=2, b=-2
$$
Answer: J
If we know that matrix $\left( \begin{matrix} {{{2 2}}} & {{{3 0}}} \\ {{{-1 2}}} & {{{a}}} \\ \end{matrix} \right)$ has an eigenvector $\left( \begin{matrix} {{-5}} \\ {{3}} \\ \end{matrix} \right)$, what is the value of $a$ ?

Options:
A. $$
- 1
$$
B. $$
- 4
$$
C. $$
- 1 8
$$
D. $$
- 8
$$
E. $$
- 1 6
$$
F. $$
- 1 0
$$
G. $$
- 1 2
$$
H. $$
- 20
$$
I. $$
- 6
$$
J. $$
- 1 4
$$
Answer: E
Let $A$ be a real symmetric matrix of order $n$ and let $P$ be an invertible matrix of order $n$ . Given that the $n$ dimensional column vector $\alpha$ is the eigenvector of $A$ belonging to the eigenvalue $\lambda$, what is the eigenvector of the matrix $(P^{-1} A P)^{T}$ belonging to the eigenvalue $\lambda$ ?

Options:
A. $$
-\alpha
$$
B. $$
P_{-1}
$$
C. $$
(P_{-1} )\, r\alpha
$$
D. $$
\, r\alpha
$$
E. $$
P \, r \alpha^2
$$
F. $$
P \alpha
$$
G. $$
-P \, r \alpha
$$
H. $$
P_{-1} \alpha
$$
I. $$
\alpha
$$
J. $$
P \, r \alpha
$$
Answer: J
Given the three-dimensional vectors $\alpha_{\mathrm{\tiny~ 1 ~}}=( 1, 1, 1 ) r \,, \alpha_{\mathrm{\tiny~ 2 ~}}=( 1,-2, 1 ) r$, there exists a non-zero vector $\alpha_{3}$ such that $\alpha_{1}, \alpha_{2}, \alpha_{3}$ form an orthogonal set of vectors. What is the value of $\alpha_{3}$?

Options:
A. $$
a_{\mathrm{{3}}}=(-1, 0, 1 ) r
$$
B. $$
a_{\mathrm{{3}}}=(-1, 0, 2 ) r
$$
C. $$
a_{\mathrm{{3}}}=(-1, 0, 3 ) r
$$
D. $$
a_{\mathrm{{3}}}=(0, 1, 1 ) r
$$
E. $$
a_{\mathrm{{3}}}=(-1, -1, 1 ) r
$$
F. $$
a_{\mathrm{{3}}}=(1, 0, 1 ) r
$$
G. $$
a_{\mathrm{{3}}}=(-1, 1, 1 ) r
$$
H. $$
a_{\mathrm{{3}}}=(1, 0, -1 ) r
$$
I. $$
a_{\mathrm{{3}}}=(-1, 0, -1 ) r
$$
Answer: A
The known characteristic value of matrix $\left( \begin{matrix} {{1}} & {{-3}} & {{3}} \\ {{3}} & {{-5}} & {{3}} \\ {{6}} & {{-6}} & {{a}} \\ \end{matrix} \right)$ is $\lambda_{{}_{1, 2}}=-2, \lambda_{{}_{3}}=4$ , so what is the value of $A$?

Options:
A. $$
a=3
$$
B. $$
a=-3
$$
C. $$
a=4
$$
D. $$
a=-4
$$
E. $$
a=-2
$$
F. $$
a=-1
$$
G. $$
a=1
$$
H. $$
a=2
$$
I. $$
a=-5
$$
J. $$
a=5
$$
Answer: C
Let the matrix $A=( \alpha_{_1}, \alpha_{_2}, \alpha_{_3}, \alpha_{_4} )$ , where $\alpha_{_{2}}, \alpha_{_{3}}, \alpha_{_{_4}}$ are linearly independent, and $\alpha_{1}=\alpha_{2}-\alpha_{3}+\alpha_{4}$ . There's a vector $\beta=\alpha_{{1}}+2 \alpha_{{2}}+3 \alpha_{{3}}+4 \alpha_{{4}} \,$. So what is the general solution to the system $A X=\beta$?

Options:
A. $$X=c (-1, 1,1, 1 ) r+( 1, 2, 3, 4 ) \tau, c\in R
$$
B. $$X=c (-1,-1,-1, 1 ) r+( 1, 2, 3, 4 ) \tau, c\in R
$$
C. $$X=c (-1, 1,-1, 1 ) r+( 1, 2, 3, 3 ) \tau, c\in R
$$
D. $$X=c (-1, 1,-1, 1 ) r+( 1, -2, 3, 4 ) \tau, c\in R
$$
E. $$X=c (-1, 1,-1, -1 ) r+( 1, 2, 3, 4 ) \tau, c\in R
$$
F. $$X=c (-1, 1,-1, 1 ) r+(-1, 2, 3, 4 ) \tau, c\in R
$$
G. $$X=c (-1, 1,-1, 1 ) r+( 1, 2, 3, 4 ) \tau, c\in R
$$
H. $$X=c (-1, 1,-1, 1 ) r+( 1, 2, -3, 4 ) \tau, c\in R
$$
I. $$X=c (-1, 1,-1, 1 ) r+( 1, 2, 3, -4 ) \tau, c\in R
$$
J. $$X=c (1, 1,-1, 1 ) r+( 1, 2, 3, 4 ) \tau, c\in R
$$
Answer: G
Let $n (n \geq 3)$ be the order of matrix $A=\left( \begin{matrix} {{{{1}}}} & {{{{a}}}} & {{{{\mathrm{L}}}}} & {{{{a}}}} \\ {{{{a}}}} & {{{{1}}}} & {{{{\mathrm{L}}}}} & {{{{a}}}} \\ {{{{\mathrm{M}}}}} & {{{{\mathrm{M}}}}} & {{{{\mathrm{M}}}}} \\ {{{{a}}}} & {{{{a}}}} & {{{{\mathrm{L}}}}} & {{{{1}}}} \\ \end{matrix} \right)$ , what is the value of $\left| A \right|$?

Options:
A. $$\left| A \right|=[ -1+( n-1 ) a ] ( 1-a )^{n-1}
$$
B. $$\left| A \right|=[ 4+( n-1 ) a ] ( 1-a )^{n-1}
$$
C. $$\left| A \right|=[ 1+( n+1 ) a ] ( 1-a )^{n-1}
$$
D. $$\left| A \right|=[ 1-( n-1 ) a ] ( 1-a )^{n-1}
$$
E. $$\left| A \right|=[ 1+( n-1 ) a ] ( 1-a )^{n+1}
$$
F. $$\left| A \right|=[ 1+( n-1 ) a ] ( 1+a )^{n-1}
$$
G. $$\left| A \right|=[ 3+( n-1 ) a ] ( 1-a )^{n-1}
$$
H. $$\left| A \right|=[ 2+( n-1 ) a ] ( 1-a )^{n-1}
$$
I. $$\left| A \right|=[ 5+( n-1 ) a ] ( 1-a )^{n-1}
$$
J. $$\left| A \right|=[ 1+( n-1 ) a ] ( 1-a )^{n-1}
$$
Answer: J
Suppose a third-order matrix $A=\left( \begin{matrix} {{{1}}} & {{{1}}} & {{{0}}} \\ {{{-2}}} & {{{-1}}} & {{{-2}}} \\ {{{-1}}} & {{{-2}}} & {{{2}}} \\ \end{matrix} \right)$ , then what are $R(A)$ and $R(A^{*})$ respectively?

Options:
A. $$R(A)=2 , R(A^{*})=3
$$
B. $$R(A)=2 , R(A^{*})=4
$$
C. $$R(A)=-3 , R(A^{*})=1
$$
D. $$R(A)=0 , R(A^{*})=2
$$
E. $$R(A)=3 , R(A^{*})=1
$$
F. $$R(A)=0 , R(A^{*})=1
$$
G. $$R(A)=1 , R(A^{*})=1
$$
H. $$R(A)=2 , R(A^{*})=1
$$
I. $$R(A)=0 , R(A^{*})=0
$$
Answer: H
Given $A P=P B$ , and $P=\left( \begin{matrix} {{{1}}} & {{{0}}} & {{{0}}} \\ {{{2}}} & {{{-1}}} & {{{0}}} \\ {{{2}}} & {{{1}}} & {{{1}}} \\ \end{matrix} \right), B=\left( \begin{matrix} {{{{1}}}} & {{{{0}}}} & {{{{0}}}} \\ {{{{0}}}} & {{{{0}}}} & {{{{0}}}} \\ {{{{0}}}} & {{{{0}}}} & {{{{-1}}}} \\ \end{matrix} \right)$ , what are the respective values of $A$ and $A^{2011}$?

Options:
A. $$A=\left( \begin{matrix} {{{1}}} & {{{0}}} & {{{0}}} \\ {{{2}}} & {{{0}}} & {{{0}}} \\ {{{6}}} & {{{-1}}} & {{{1}}} \\ \end{matrix} \right), A^{2 0 1 3}=A
$$
B. $$A=\left( \begin{matrix} {{{1}}} & {{{0}}} & {{{0}}} \\ {{{2}}} & {{{0}}} & {{{0}}} \\ {{{6}}} & {{{-1}}} & {{{-1}}} \\ \end{matrix} \right), A^{2 0 1 0}=A
$$
C. $$A=\left( \begin{matrix} {{{1}}} & {{{0}}} & {{{0}}} \\ {{{2}}} & {{{0}}} & {{{0}}} \\ {{{6}}} & {{{-1}}} & {{{-1}}} \\ \end{matrix} \right), A^{2 0 1 3}=A
$$
D. $$A=\left( \begin{matrix} {{{1}}} & {{{0}}} & {{{0}}} \\ {{{2}}} & {{{0}}} & {{{0}}} \\ {{{6}}} & {{{-1}}} & {{{1}}} \\ \end{matrix} \right), A^{2 0 1 0}=A
$$
E. $$A=\left( \begin{matrix} {{{1}}} & {{{0}}} & {{{0}}} \\ {{{2}}} & {{{0}}} & {{{0}}} \\ {{{6}}} & {{{-1}}} & {{{1}}} \\ \end{matrix} \right), A^{2 0 1 2}=A
$$
F. $$A=\left( \begin{matrix} {{{1}}} & {{{0}}} & {{{0}}} \\ {{{2}}} & {{{0}}} & {{{0}}} \\ {{{6}}} & {{{-1}}} & {{{-1}}} \\ \end{matrix} \right), A^{2 0 1 2}=A
$$
G. $$A=\left( \begin{matrix} {{{1}}} & {{{0}}} & {{{0}}} \\ {{{2}}} & {{{0}}} & {{{0}}} \\ {{{6}}} & {{{-1}}} & {{{-1}}} \\ \end{matrix} \right), A^{2 0 1 4}=A
$$
H. $$A=\left( \begin{matrix} {{{1}}} & {{{0}}} & {{{0}}} \\ {{{2}}} & {{{0}}} & {{{0}}} \\ {{{6}}} & {{{-1}}} & {{{1}}} \\ \end{matrix} \right), A^{2 0 1 4}=A
$$
I. $$A=\left( \begin{matrix} {{{1}}} & {{{0}}} & {{{0}}} \\ {{{2}}} & {{{0}}} & {{{0}}} \\ {{{6}}} & {{{-1}}} & {{{-1}}} \\ \end{matrix} \right), A^{2 0 1 1}=A
$$
J. $$A=\left( \begin{matrix} {{{1}}} & {{{0}}} & {{{0}}} \\ {{{2}}} & {{{0}}} & {{{0}}} \\ {{{6}}} & {{{-1}}} & {{{1}}} \\ \end{matrix} \right), A^{2 0 1 1}=A
$$
Answer: I
What is the result of calculating the determinant $D_{n}=\left| \begin{matrix} {{{x}}} & {{{0}}} & {{{0}}} & {{{\mathrm{L}}}} & {{{0}}} & {{{a_{0}}}} \\ {{{-1}}} & {{{x}}} & {{{0}}} & {{{\mathrm{L}}}} & {{{0}}} & {{{a_{1}}}} \\ {{{0}}} & {{{-1}}} & {{{x}}} & {{{\mathrm{L}}}} & {{{0}}} & {{{a_{2}}}} \\ {{{\mathrm{M}}}} & {{{\mathrm{M}}}} & {{{\mathrm{M}}}} & {{{}}} & {{{\mathrm{M}}}} & {{{\mathrm{M}}}} \\ {{{0}}} & {{{0}}} & {{{0}}} & {{{\mathrm{L}}}} & {{{x}}} & {{{a_{n-2}}}} \\ {{{0}}} & {{{0}}} & {{{0}}} & {{{\mathrm{L}}}} & {{{-1}}} & {{{x+a_{n-1}}}} \\ \end{matrix} \right|$ of order $n$?

Options:
A. $$x_{n}+a_{n-1} x_{n-1}+\mathrm{L} \ -a_{1} x+a_{0} \ .
$$
B. $$x_{n}-a_{n-1} x_{n-1}+\mathrm{L} \ +a_{1} x-a_{0} \ .
$$
C. $$x_{n}+a_{n-1} x_{n-1}-\mathrm{L} \ +a_{1} x+a_{0} \ .
$$
D. $$x_{n}-a_{n-1} x_{n-1}-\mathrm{L} \ +a_{1} x+a_{0} \ .
$$
E. $$x_{n}+a_{n-1} x_{n-1}+\mathrm{L} \ +a_{1} x+a_{0} \ .
$$
F. $$2x_{n}+a_{n-1} x_{n-1}+\mathrm{L} \ +a_{1} x+a_{0} \ .
$$
G. $$x_{n}+a_{n-1} x_{n-1}+\mathrm{L} \ +a_{1} x-a_{0} \ .
$$
H. $$x_{n}-a_{n-1} x_{n-1}+\mathrm{L} \ -a_{1} x+a_{0} \ .
$$
I. $$x_{n}-a_{n-1} x_{n-1}+\mathrm{L} \ +a_{1} x+a_{0} \ .
$$
J. $$x_{n}+2a_{n-1} x_{n-1}+\mathrm{L} \ +a_{1} x+a_{0} \ .
$$
Answer: E
In the path expression of the object query language, if a represents an object of some class and p represents a method, then a.p represents ( ).

Options:
A. Apply p to the result of a
B. Calculate p based on the instance a
C. the value of this attribute of a
D. Execute p on the evaluation of a
E. Retrieve p using the object a
F. Access p through the reference a
G. Compute p using the output of a
H. Functions related to this class
I. Return p from the attribute a
J. The object associated with a
Answer: A
With schema/in-schema images, you can ensure that the () between data and applications.

Options:
A. Network efficiency
B. Access latency
C. Data security
D. Physical independence
E. Logical independence
F. Data consistency
G. System scalability
H. User integrity
I. Data redundancy
J. Storage optimization
Answer: D
Which of the following descriptions of unlocking and retaining locks in a transaction process is correct?

Options:
A. The S lock must be retained until the end of the transaction to avoid losing updates; The X blockade can be lifted at any time to increase concurrency.
B. The X block can be lifted at any time to increase concurrency; The S lock must be retained until the end of the transaction to avoid losing updates.
C. All types of blockades can be lifted at any time to increase concurrency.
D. All types of lockouts must be retained until the end of the transaction to avoid live locks.
E. X blockade can be lifted at any time to reduce waiting time; The S lock must be retained until the end of the transaction to avoid deadlock.
F. The S lock must be retained until the end of the transaction to avoid live locks; The X blockade can be lifted at any time to reduce waiting time.
G. All types of blockades must be retained until the end of the transaction to prevent deadlocks.
H. The X lock must be retained until the end of the transaction to avoid losing updates; The S blockade can be lifted at any time to increase concurrency.
I. All types of lockouts must be retained until the end of the transaction to ensure data consistency.
J. All types of blockades can be lifted at any time to reduce waiting times.
Answer: H
In a relational calculus formula, which has the highest priority within the same parentheses?

Options:
A. Aggregation calculation operator
B. Sequential execution operator
C. Logical operator
D. Multiplicative addition operator
E. Existential quantifiers
F. Subquery relational operator
G. Conditional branching operator
H. Concatenation string operator
I. Arithmetic comparison operator
J. Universal quantifiers
Answer: I
The division principle of hierarchical model, network model and relational model is ( ).

Options:
A. Connections between data
B. Volume of data stored
C. Number of user queries
D. Data processing speed
E. Complexity of the connection
F. Type of storage device
G. Record length
H. Number of tables used
I. Data access frequency
J. Size of the file
Answer: A
The key issue of the recovery mechanism is ( ).

Options:
A. Improved access controls
B. Periodic system updates
C. Reinforce network speed
D. Multiple server locations
E. Data mirroring
F. Data dump
G. Enhanced security protocols
H. Advanced encryption methods
I. Register log files
J. Create redundant data
Answer: J
The method to determine whether a system is a distributed database system is ( ).

Options:
A. Support global applications
B. Has low transaction latency
C. Maintains data copies securely
D. Adopt C/S structure
E. High data independence
F. Data is localized to single server
G. Data is distributed and stored in multiple sites
H. Data is replicated across multiple nodes
I. Uses multiple database schemas
J. Operates with a single database server
Answer: A
In a parallel database, the tables are split onto different disks. The following split that are best for full table scanning is ( ).

Options:
A. Rotation method
B. Distribution technique
C. Range allocation
D. Segment separation
E. Boundary segmentation
F. Sequence splitting
G. Equivalence division
H. Hash partition
I. Parallel distribution
J. Scope division
Answer: G
We use TB (T1) to represent the start time of transaction T and TC (T1) to represent the commit time of transaction T. The following five transactions exist:
TB(T1) = 10, TC(T1) = 30
TB(T2) = 50, TC(T2) = 100
TB(T3) = 80, TC(T3) = 200
TB(T4) = 120, TC(T4) = 150
TB(T5) = 180, TC(T5) = 220
The system generates a checkpoint at time point 90, and a system fault occurs at time point 190. In the process of system fault recovery, you need to ().

Options:
A. Redo T4 and T5, undo T1 and T2
B. Redo T1, T2, T4, and undo T3, T5
C. Redo T1 and T2, undo T3 and T5
D. Redo T3 and T4, undo T1 and T2
E. Redo T1, T2, T3, undo T4, T5
F. Redo T2 and T5, undo T3 and T4
G. Redo T2 and T4, undo T3 and T5
H. Redo T2 and T3, undo T4 and T5
I. Redo T1 and T3, undo T2 and T4
J. Redo T1 and T4, undo T2 and T3
Answer: G
It is known that the relationship pattern R (A,B,C,D,E) and the set of functional relationships on it $\mathrm{F=\{A \to D, ~ B \to C ~, ~ E \to A}\}$. The candidate keyword for this relational pattern is ().

Options:
A. BD
B. AD
C. EC
D. DE
E. AB
F. AC
G. CD
H. BE
I. EA
J. EBC
Answer: H
Data management technology has gone through three stages: (), (), and ().

Options:
A. Artificial management; file system; database system
B. Distributed Processing; Cloud Computing; Big Data Technology
C. Technical Support; System Analysis; Program Development
D. Data compilation; file indexing; system management
E. Data storage; indexing methods; management software
F. Information architecture; content system; data architecture
G. Information Entry; Storage Solutions; Information Platform
H. Program Design; Network Configuration; Database Application
I. Automated management; network system; multimedia system
J. Spreadsheets; Data Collection; Text Processing
Answer: A
Suppose there is a staff table that contains "gender" spontaneity and requires that the value of this attribute can only be "male" or "female", which belongs to ().

Options:
A. Relationship invariance
B. Data consistency
C. User-defined integrity
D. Data redundancy
E. Logical integrity
F. Transaction consistency
G. referential integrity
H. Entity integrity
I. Functional integrity
J. Domain integrity
Answer: C
In the development process of data management technology, data independence is highest in the () stage.

Options:
A. Database system
B. Data warehouse
C. Data grid
D. Distributed database
E. Active database
F. Data item management
G. File system
H. Manual management
I. Object relational database
J. Data Lake
Answer: A
Which of the following is the correct way to find the minimum connectivity scheme (minimum spanning tree) that includes a specified set of edges?

Options:
A. The primary edge set of the minimum tree includes no specified edges, and all weights are set to zero. Check each edge in turn.
B. The primary edge set of the minimum tree consists of all edges sorted by descending weight, and the remaining are checked in ascending order.
C. The primary edge set of the minimum tree is the midpoint weight edge, and the weights of remaining edges fluctuate randomly. Check them one by one.
D. The primary edge set of the minimum tree is the set of all specified edges. The permissions of the remaining edges are as large as possible. Check them one by one.
E. The primary edge set of the minimum tree is the smallest weight edge, and the weights of the remaining edges are increased to the largest. Check a series of them one by one.
F. The primary edge set of the minimum tree is randomly selected, and the weights of the other edges are minimized. Check each in sequence.
G. The primary edge set of the minimum tree is the smallest specified edge of power, and the power of the remaining edges is from large to large. Check them one by one.
H. The primary edge set of the minimum tree is the average of all specified edges, with remaining edges given random weights. Check each one systematically.
I. The primary edge set of the minimum tree is the largest weight edge, and the weights of the remaining edges are decreased to the smallest. Check a series of them one by one.
J. The primary edge set of the minimum tree is the first specified edge, and the power of the remaining edges increases, and a few are checked one by one.
Answer: D
There are several statements regarding the understanding of Gauss's law. Which of the following is correct?

Options:
A. If there is no net charge inside the Gaussian surface, the electric flux through the surface must be non-zero.
B. If $\tilde{E}$ is zero everywhere on the Gaussian surface, there must be no charge inside the surface.
C. If there is net charge outside the Gaussian surface, the electric flux through the surface must be zero.
D. If $\tilde{E}$ is not zero everywhere on the Gaussian surface, there must be charge inside the surface.
E. If the electric flux through the Gaussian surface is zero, there must be charge inside the surface.
F. If there is no charge inside the Gaussian surface, $\tilde{E}$ must be zero everywhere on the surface.
G. If there is net charge inside the Gaussian surface, the electric flux through the surface must be non-zero.
H. If there is no net charge inside the Gaussian surface, the electric flux through the surface must be zero.
Answer: G
A particle with charge $q$ moves in a uniform magnetic field. Which of the following statements is correct?

Options:
A. If the particle's velocity is halved, the magnetic force is proportionally reduced.
B. Despite different charges, the magnetic force experienced by all particles is identical.
C. After the particle enters the magnetic field, both its kinetic energy and momentum remain unchanged.
D. If the particle's velocity is consistent, changing $q$ to $-q$ aligns the forces directionally.
E. Provided the speed remains constant, switching $q$ to $-2q$ duplicates both direction and magnitude of the force
F. Since the Lorentz force is perpendicular to the direction of velocity, the trajectory of the charged particle must be circular.
G. Provided the speed is doubled, changing $q$ to $-q$ doubles the Lorentz force.
H. If the speed is consistent, changing $q$ to $2q$ doubles the Lorentz force.
I. Only if the speed is the same will the Lorentz force on the particle be the same.
J. Under the premise of constant speed, if the charge $q$ changes to $-q$, the force on the particle reverses direction but remains the same in magnitude.
Answer: J
For a one-dimensional monoatomic lattice, under the simple harmonic approximation, consider that each atom interacts with all other atoms. Calculate the dispersion relation of the lattice wave______.

Options:
A. $$ M \omega^{2}=\sum_{m=1}^{\infty} \beta_{m} \left( e^{i q m a}+e^{-i q m a}-1 \right) $$
B. $$ - M \omega^{2}=\sum_{m=1}^{\infty} \beta_{m} \left( e^{i q m a}+e^{-i q m a}-2 \right) $$
C. $$ - M \omega^{2}=\sum_{m=1}^{\infty} \beta_{m} \left( e^{i q m a}+e^{-i q m a}-12 \right) $$
D. $$ M \omega^{2}=\sum_{m=1}^{\infty} \beta_{m} \left( e^{i q m a}+e^{-i q m a}-2 \right) $$
E. $$ M \omega^{2}=\sum_{m=1}^{\infty} \beta_{m} \left( e^{i q m a}+e^{-i q m a}-7 \right) $$
F. $$ - M \omega^{2}=\sum_{m=1}^{\infty} \beta_{m} \left( e^{i q m a}+e^{-i q m a}-11 \right) $$
G. $$ M \omega^{2}=\sum_{m=1}^{\infty} \beta_{m} \left( e^{i q m a}+e^{-i q m a} \right) $$
H. $$ - M \omega^{2}=\sum_{m=1}^{\infty} \beta_{m} \left( e^{i q m a}+e^{-i q m a}-1 \right) $$
I. $$ - M \omega^{2}=\sum_{m=1}^{\infty} \beta_{m} \left( e^{i q m a}-2e^{-i q m a}-1 \right) $$
J. $$ - M \omega^{2}=\sum_{m=1}^{\infty} \beta_{m} \left( e^{i q m a}+e^{-i q m a} \right) $$
Answer: B
When electrons occupy all the states in an energy band, the band is called (); when no electrons occupy an energy band, it is called (); the first full band below the conduction band, or the uppermost full band, is called is (); the lowest empty band is called (); the width of the energy level that is not allowed to exist between the two energy bands is called ().

Options:
A. Empty belt; Full belt; Guide belt; Belt gap; Price belt
B. Full Belt; Price Belt; Guide Belt; Empty Belt; Belt Gap
C. Full belt; Price belt; Empty belt; Guide belt; Belt gap
D. Full Belt; Price Belt; Guide Belt; Band Gap; Void Belt
E. Full belt; Empty belt; Guide belt; Belt gap; Price belt
F. Full belt; Empty belt; Price belt; Guide belt; Belt gap.
G. Price belt; Full belt; Empty belt; Guide belt; Belt gap
H. Empty belt; Full belt; Price belt; Belt gap; Guide belt.
I. Full belt; Empty belt; Guide belt; Price belt; Belt gap.
Answer: F
The experimental value of $\mathrm{A l}$ plasma energy $\hbar\omega_{p}$ is 15.3eV, and the electron density according to the free electron gas model is $\mathbf{n}=\mathbf{1 8. 0 6 \times1 0^{2 2} m^{-3}}$ , find the theoretical value of $\hbar\omega_{p}$ ( )

Options:
A. 15.7eV
B. 16.5eV
C. 16.1eV
D. 15.4eV
E. 15.2eV
F. 15.8eV
G. 15.5eV
H. 15.9eV
I. 15.6eV
J. 16.0eV
Answer: A
What kind of crystal structure do general metals have? What is the maximum coordination number?

Options:
A. Cubic close-packed structure and square structure; 10
B. Body-centered cubic structure and hexagonal structure.
C. Cubic close-packed structure and pentagonal structure;12
D. Cubic close-packed structure and square structure; 12
E. Body-centered cubic structure and hexagonal close-packed structure; 10
F. Cubic close-packed structure and hexagonal structure; 10
G. Cubic close-packed structure and hexagonal close-packed structure; 12
H. Body-centered cubic structure and square structure; 12
I. Face-centered cubic structure and body-centered cubic structure;12
J. Face-centered cubic structure and hexagonal close-packed structure; 12
Answer: J
The vibrational mode density $$g ( \omega) $$ of a one-dimensional monoatomic chain =________.

Options:
A. $$ \frac{N} {\pi} \left( {\omega_{m}}^{2}+{\omega}^{2} \right)^{\frac{1} {2}} $$
B. $$ \frac{N} {\pi} \left( {\omega_{m}}^{2}-{\omega}^{2} \right)^{\frac{1} {2}} $$
C. $$ \frac{2 N} {\pi} \left( {\omega_{m}}^{2}- 2{\omega}^{2} \right)^{\frac{1} {2}} $$
D. $$ \frac{N} {\pi} \left( {\omega_{m}}^{3}-{\omega}^{3} \right)^{\frac{1} {2}} $$
E. $$ \frac{N} {\pi} \left( {\omega_{m}}^{2}-{\omega}^{3} \right)^{\frac{1} {2}} $$
F. $$ \frac{2 N} {\pi} \left( {\omega_{m}}^{2}-{\omega}^{2} \right)^{\frac{1} {2}} $$
G. $$ \frac{2 N} {\pi} \left( {\omega_{m}}^{4}-{\omega}^{4} \right)^{\frac{1} {2}} $$
H. $$ \frac{N} {\pi} \left( {\omega_{m}}^{2}- 3{\omega}^{2} \right)^{\frac{1} {2}} $$
I. $$ \frac{N} {\pi} \left( {\omega_{m}}^{2}+\frac{1}{2}{\omega}^{2} \right)^{\frac{1} {2}} $$
Answer: F
It is known that copper (Z=29) has a wavelength of 0.154mm for its $K_{\alpha}$ line, and the shielding constant $\sigma$ for its $\mathbf{K}$ shell electron is ________.

Options:
A. 0.9432
B. 0.9113
C. 0.6986
D. 0.7794
E. 0.8251
F. 0.9395
G. 1.1072
H. 0.9213
I. 0.8901
J. 1.0255
Answer: B
What does it indicate if the output voltage of amplifier A is smaller under open-load conditions, given that amplifiers A and B have the same gain but different input and output resistances and use the same signal source with internal resistance?

Options:
A. The output resistance of B is high
B. The output resistance of A is low
C. The output resistance of A is high
D. The input resistance of B is high
E. The gain of amplifier A is high
F. The input resistance of A is high
G. The output resistance of B is low
H. The input resistance of A is low
I. The input resistance of B is low
Answer: H
Melting $1 ~ \mathbf{k g} ~ 0$ °C ice into 100°C water, the heat of fusion of the ice is $3. 3 5 \times1 0^{5} \ \ \mathrm{J} \cdot\mathrm{k g}^{-1}$ , and the specific constant-pressure heat capacity of water is $4 . 1 8 \times1 0^{3} \ \mathrm{J} \cdot\mathrm{k g}^{-1} \cdot\mathrm{K}^{-1}$ , and its entropy becomes ____.

Options:
A. $2 \; 0 0 0 \; \mathrm{J} \cdot{\bf K}^{-1}$
B. $2 \; 5 4 0 \; \mathrm{J} \cdot{\bf K}^{-1}$
C. $2 \; 4 0 0 \; \mathrm{J} \cdot{\bf K}^{-1}$
D. $1 \; 8 7 5 \; \mathrm{J} \cdot{\bf K}^{-1}$
E. $2 \; 4 8 8 \; \mathrm{J} \cdot{\bf K}^{-1}$
F. $2 \; 7 3 2 \; \mathrm{J} \cdot{\bf K}^{-1}$
G. $2 \; 5 3 2 \; \mathrm{J} \cdot{\bf K}^{-1}$
H. $2 \; 5 5 5 \; \mathrm{J} \cdot{\bf K}^{-1}$
I. $2 \; 6 5 0 \; \mathrm{J} \cdot{\bf K}^{-1}$
J. $2 \; 6 2 0 \; \mathrm{J} \cdot{\bf K}^{-1}$
Answer: G
The average lifetime of a particle at rest is experimentally measured to be $\Delta t^{\prime}$, and the average distance traveled is $v \Delta t$ when it is moving at a speed $\mathbf{v}$ much less than the speed of light. However, if $\mathbf{v}$ is close to the speed of light, the experimentally measured distance traveled by most of the particle is much greater than $v \Delta t$, and this experimental result suggests that ___.

Options:
A. At greater speeds, the time expansion phenomenon occurs.
B. When velocity approaches light speed, time extension is noted.
C. Near light speed, direct time reduction happens.
D. With higher velocities, temporal dilation is observed.
E. In reduced velocity cases, spatial expansion is noted.
F. At lower speeds, the time contraction effect occurs.
G. During high-speed motion, there is a time dilation effect.
H. As speed increases, there is a dilation in time.
I. With increased motion, a spatial compression effect arises.
J. At an advanced speed, there is a space distortion effect.
Answer: G
An electron starts from rest and passes through a uniform electric field with a potential difference of $1. 0 0 \times1 0^{4}$ V. The electron is accelerated, and the rest mass of the electron is known to be $m_{0}=9. 1 1 \times1 0^{-3 1}$ kg. Q: What is the speed of the electron after it is accelerated?

Options:
A. $2. \, 5 6 \times1 0^{8} \, ( \mathrm{m} \cdot\mathrm{s}^{-1} )$
B. $4. \, 1 2 \times1 0^{6} \, ( \mathrm{m} \cdot\mathrm{s}^{-1} )$
C. $7. \, 9 2 \times1 0^{6} \, ( \mathrm{m} \cdot\mathrm{s}^{-1} )$
D. $8. \, 4 4 \times1 0^{6} \, ( \mathrm{m} \cdot\mathrm{s}^{-1} )$
E. $6. \, 7 0 \times1 0^{7} \, ( \mathrm{m} \cdot\mathrm{s}^{-1} )$
F. $3. \, 9 6 \times1 0^{7} \, ( \mathrm{m} \cdot\mathrm{s}^{-1} )$
G. $5. \, 8 5 \times1 0^{7} \, ( \mathrm{m} \cdot\mathrm{s}^{-1} )$
H. $9. \, 4 3 \times1 0^{7} \, ( \mathrm{m} \cdot\mathrm{s}^{-1} )$
I. $3. \, 7 5 \times1 0^{9} \, ( \mathrm{m} \cdot\mathrm{s}^{-1} )$
J. $4. \, 7 2 \times1 0^{7} \, ( \mathrm{m} \cdot\mathrm{s}^{-1} )$
Answer: G
In an inertial system $\mathbf{S}$$ in vacuum, a light source is located at the midpoint of the line connecting two optical signal receivers, all three of which are stationary in the S-system. Let the signal receivers in the S-system be all 3km away from the light source, and each receives a pulse of light from the light source at the same time. The time interval between the reception of the two pulses in the S' system, which is moving at a speed of $\mathrm{c} / 2$ with respect to the $\mathbf{S}$ system, is ____.

Options:
A. $4.9 \times 10^{-8} \mathrm{~ s}$
B. $4.6 \times 10^{-8} \mathrm{~ s}$
C. $6.5 \times 10^{-8} \mathrm{~ s}$
D. $4.3 \times 10^{-8} \mathrm{~ s}$
E. $5. 8 \times1 0^{-8} \mathrm{~ s}$
F. $9.2 \times 10^{-8} \mathrm{~ s}$
G. $3.4 \times 10^{-8} \mathrm{~ s}$
H. $6.2 \times 10^{-8} \mathrm{~ s}$
I. $2.3 \times 10^{-8} \mathrm{~ s}$
J. $7.5 \times 10^{-8} \mathrm{~ s}$
Answer: E
Try to find the pH of a mixture of 300mL of 0.50mo/L H3 PO4 and 500mL of 0.50mol/L NaOH is ____.

Options:
A. 7.51
B. 7.23
C. 8.11
D. 8.35
E. 6.95
F. 7.44
G. 7.68
H. 6.80
I. 7.92
J. 7.85
Answer: A
What different positions do protons occupy in molecules, and what different phenomena is termed magnetic anisotropy?

Options:
A. Atomic placement, polar disparity
B. Orbital location, magnetic polarity
C. Spatial position, shielding effect
D. Nuclear alignment, magnetic variation
E. Electron configuration, field anis
F. Electron configuration, resonance effect
G. Chemical arrangement, electric variance
H. Atomic placement, resonance impact
I. Nuclear alignment, diamagnetic response
J. Molecular orientation, polar disparity
Answer: C
The UV absorption peaks of saturated hydrocarbons are in what range?

Options:
A. Low Ultraviolet Field
B. Far Ultraviolet Region
C. Near Infrared Spectrum
D. Deep Ultraviolet Region
E. Wide Microwave Range
F. Broad Infrared Band
G. Mid Ultraviolet Spectrum
H. High Ultraviolet Area
I. High Energy X-ray Zone
J. Shallow Ultraviolet Section
Answer: B
What are the horizontal and vertical coordinates of the Hertzsprung-Russell diagram?

Options:
A. Gravitational Pull and Magnetic Field
B. Mass and Density
C. Rotation and Revolution
D. Distance and Motion
E. Surface Temperature and Atmospheric Pressure
F. Spectral and Photometric Types
G. Energy Output and Chemical Makeup
H. Size and Composition
I. Color and Brightness Levels
J. Temperature and Luminosity
Answer: F
The time interval between the first and second quarter moons is roughly ( ) months.

Options:
A. 0.8
B. 0.9
C. 1.5
D. 1.2
E. 1
F. 0.6
G. 1.3
H. 2
I. 0.7
J. 0.5
Answer: J
When a supernova explodes, its brightness changes by more than () magnitude.

Options:
A. 10
B. 18
C. 12
D. 25
E. 20
F. 30
G. 22
H. 15
I. 24
J. 28
Answer: E
In what part of the galaxy is the Sun located?

Options:
A. Silver halo
B. Silver disk
C. Silver belt
D. Silver plate
E. Silver crown
F. Silver nuclei
G. Silver orbit
H. Silver shell
I. Silver core
J. Silver rim
Answer: D
Using a logarithmic transformation curve can achieve the purpose of compressing the dynamic range of image grayscale. What is the reason for this?

Options:
A. The range of grayscale values changes before and after transformation.
B. The dynamic range adjustment adjusts all the pixel intensities.
C. The change in grayscale values requires a logarithmic equation.
D. The computation outputs altered grayscale values in a linear way.
E. The transformation curve in logarithmic form is a monotonically increasing curve.
F. The transformation takes only a portion of the range of grayscale values.
G. The curve compresses all colors not just grayscale levels.
H. The transformation multiplies each grayscale value by a constant.
I. The range of grayscale values before the transformation is larger than the range after the transformation.
J. The transformation involves squaring the pixels' brightness levels.
Answer: F
Which of the following statements about image magnification processing is correct?

Options:
A. Enlarging an image does not cause distortion of the image.
B. When the magnification factor is relatively small, using an image enlargement method based on pixel magnification principles will result in a mosaic effect.
C. If image magnification does not involve pixel interpolation, there will be no loss of clarity.
D. The process of image magnification is unrelated to computational algorithm efficiency.
E. Image enlargement and reduction are processes independent of resolution changes.
F. When dealing with high magnification factors, simple enlargement techniques avoid pixelation.
G. Image magnification methods rely solely on the addition of new image data points.
H. In the digital realm, image reduction is the complex operation to image enlargement.
I. For the issue of unnatural image effects caused by the transition between enlarged image sub-blocks being uneven, the bilinear interpolation method cannot be used to solve it.
J. In the physical sense, image enlargement is the inverse operation of image reduction.
Answer: J
The compression of vector space data is mainly realized by ().

Options:
A. Deploy a matrix operation to integrate redundant data points within the central axis or margin of spatial zones.
B. Utilize a conversion algorithm to enhance select coordinates on the peripheries or edges of spatial domains.
C. Store graphic data and attribute data separately.
D. Implement a sequence strategy to modify key nodes on the edges or vertices of polygonal areas.
E. Execute a compression technique to expand certain vertices on the boundaries or outlines of defined areas.
F. Apply a reduction formula to insert additional vertices along the contours or perimeters of geometric structures.
G. Conduct a procedural method to replace certain vertices on the extremities or outlines of bounded territories.
H. Establish the topological relationships between graphical elements.
I. Travel coding, quadtree coding, and other methods.
J. Utilize a certain algorithm to delete some coordinate points on the features or boundaries of thread-bound regions.
Answer: J
The Maritime Silk Road refers to the ancient sea route from China to the Southwest Pacific and ____. It experienced three historical periods: the Western Han, Tang Dynasty, and Ming Dynasty.

Options:
A. Eastern Europe
B. Indian Ocean
C. South America
D. Northern Africa
E. Eastern Mediterranean
F. Western Sahara
G. Caribbean Sea
H. Southern Arctic
I. Central Asia
J. North Atlantic
Answer: B
The landscape formed by intangible, invisible cultural features is called a _______landscape. This type of cultural landscape cannot be captured in photographs nor displayed on ordinary maps.

Options:
A. non-visible cultural
B. conceptual cultural
C. abstract cultural
D. invisible natural
E. intangible complex
F. non-corporeal cultural
G. notional cultural
H. non-physical cultural
I. non-material cultural
J. non-tangible cultural
Answer: I
______is the science that studies the spatial and temporal laws of human phenomena on the Earth's surface.

Options:
A. Urban ethnography
B. Human geography
C. Behavioral economics
D. Comparative politics
E. Political history
F. Environmental sociology
G. Economic sociology
H. Physical geography
I. Cultural anthropology
J. Social psychology
Answer: B
The forms, methods, procedures, structures, and other overall terms for human behavior are collectively referred to as modes of________.

Options:
A. environmental adaptation
B. physical movement
C. religious observance
D. geographical distribution
E. educational practice
F. human behavior
G. societal interaction
H. mental processing
I. cultural expression
J. technological usage
Answer: F
______ refers to the pattern formed by the combination, proportion, and interconnections of various land types within a specific regional unit. It reflects the characteristics of entirety and stability within a natural regional unit.

Options:
A. Land makeup
B. Land configuration
C. Geographical formation
D. Land composition
E. Earth framework
F. Soil arrangement
G. Ground texture
H. Landscape setup
I. Terrain pattern
J. Land structure
Answer: J
_______water in soil is one type of soil water. After the film water is filled, the moisture retained in the capillary pores through capillary action (curved liquid surface tension) is called capillary water.

Options:
A. Atmospheric
B. Surface
C. Capillary
D. Gravitational
E. Interstitial
F. Bound
G. Percolating
H. Saturated
I. Hydroscopic
J. Adsorbed
Answer: C
The airflow of radial motion is influenced by the Coriolis effect, causing different wind directions to prevail in different zones at the Earth's surface. This type of wind is known as the ________.

Options:
A. oceanic breeze boundary
B. continental draft region
C. polar gust strip
D. hemisphere gust belt
E. trade winds belt
F. meridional wind sector
G. planetary wind band
H. tropical breeze zone
I. equatorial flow line
J. global current circle
Answer: E