A water pumping station found that its electricity consumption (unit: kilowatt-hours) is directly proportional to the cube of the pump motor speed (unit: rpm). Based on this, which of the following five graphs best describes the relationship between the electricity consumption $y$ (kilowatt-hours) and the pump motor speed $X$ (rpm) of this water pumping station?
(1) [Graph 1] (2) [Graph 2] (3) [Graph 3] (4) [Graph 4] (5) [Graph 5]

Consider a real $2 \times 2$ matrix $\left[ \begin{array} { l l } a & b \\ c & d \end{array} \right]$. If $\left[ \begin{array} { l l } 0 & 1 \\ 1 & 0 \end{array} \right] \left[ \begin{array} { l l } a & b \\ c & d \end{array} \right] \left[ \begin{array} { c c } 1 & 0 \\ 0 & - 2 \end{array} \right] = \left[ \begin{array} { c c } 3 & - 4 \\ - 9 & - 7 \end{array} \right]$, what is the value of $c - 2b$?
(1) $- 11$ (2) $- 4$ (3) $1$ (4) $10$ (5) $11$

There are two tall buildings on the ground, Building A and Building B. It is known that Building A is taller than Building B, and the horizontal distance between the two buildings is 150 meters. A person pulls a rope from the top of Building A to the top of Building B, and measures the angle of depression to the top of Building B from the top of Building A as $22^{\circ}$. Assuming the rope is pulled straight, which of the following options is closest to the length of the rope (unit: meters)? (Note: The angle of depression is the angle between the line of sight and the horizontal line when looking down at an object)
(1) $150$ (2) $150 \sin 22^{\circ}$ (3) $150 \cos 22^{\circ}$ (4) $\frac{150}{\cos 22^{\circ}}$ (5) $\frac{150}{\sin 22^{\circ}}$

A school's midterm examination has 29 test takers, and all scores are different. After statistics, the scores at the 25th, 50th, 75th, and 95th percentiles are 41, 60, 74, and 92 points respectively. Later, it was discovered that the scores needed adjustment. The scores of the top 15 students with higher scores should each be increased by 5 points, while the remaining students' scores remain unchanged. Assuming the adjusted scores at the 25th, 50th, 75th, and 95th percentiles are $a$, $b$, $c$, and $d$ points respectively, which of the following options is the tuple $(a, b, c, d)$?
(1) $(41,60,74,92)$ (2) $(41,60,74,97)$ (3) $(41,65,79,97)$ (4) $(46,65,79,92)$ (5) $(46,65,79,97)$

A bag contains 100 balls numbered $1, 2, \ldots, 100$ respectively. A person randomly draws one ball from the bag, and each ball has an equal probability of being drawn. Under which of the following conditions is the conditional probability that the person draws ball number 7 the largest?
(1) The number of the ball drawn is odd (2) The number of the ball drawn is prime (3) The number of the ball drawn is a multiple of 7 (4) The number of the ball drawn is not a multiple of 5 (5) The number of the ball drawn is less than 10

A person calculates the remainder when the polynomial $f(x) = x^{3} + ax^{2} + bx + c$ is divided by $g(x) = ax^{3} + bx^{2} + cx + d$, where $a, b, c, d$ are real numbers and $a \neq 0$. He mistakenly read it as $g(x)$ divided by $f(x)$, and after calculation obtained the remainder as $-3x - 17$. Assuming the correct remainder when $f(x)$ is divided by $g(x)$ equals $px^{2} + qx + r$, what is the value of $p$?
(1) $-3$ (2) $-1$ (3) $0$ (4) $2$ (5) $3$

A flashlight's light beam forms a right circular cone with a light divergence angle of $60^{\circ}$, as shown in the figure. The wall is perpendicular to the floor, and their intersection is a straight line $L$. The flashlight is directed perpendicular to $L$, meaning the axis of the right circular cone is perpendicular to $L$. If the edge of the light beam on the wall is part of a parabola, then the edge of the light beam on the floor is part of which of the following shapes?
(1) Two intersecting lines (2) Circle (3) Parabola (4) Ellipse with unequal major and minor axes (5) Hyperbola

An electronic billboard continuously alternates between playing advertisements A and B ($A$, $B$, $A$, $B \ldots$), with each advertisement playing for $T$ minutes (where $T$ is an integer). A person passes by just as advertisement A starts playing. 30 minutes later, the person returns to the location and sees advertisement B just starting to play. Select the options that could be the value of $T$.
(1) $15$ (2) $10$ (3) $8$ (4) $6$ (5) $5$

Given $a = 6$, $b = \frac{20}{3}$, $c = 2\sqrt{10}$, and $d$, where $d$ is a rational number. These four numbers are marked on a number line as $A(a)$, $B(b)$, $C(c)$, and $D(d)$. Select the correct options.
(1) $a + b + c + d$ must be a rational number (2) $abcd$ must be an irrational number (3) Point $D$ could possibly be at a distance of $2\sqrt{10} + 6$ from point $C$ (4) The midpoint of points $A$ and $B$ is to the right of point $C$ (5) Among all points on the number line at a distance less than 8 from point $B$, there are 14 positive integers and 1 negative integer

An organization introduced two different nutrients into culture dishes A and B at 12 o'clock. At this time, the bacterial counts in dishes A and B are $X$ and $Y$ respectively. The quantity in dish A doubles every 3 hours; for example, at 3 PM the quantity in A is $2X$. The quantity in dish B doubles every 2 hours; for example, at 2 PM the quantity in B is $2Y$, and at 4 PM the quantity in B is $4Y$. Part of the measurement results are recorded in the table below. At 6 PM, the organization measured that the quantities in dishes A and B are the same. To estimate the bacterial quantities in dishes A and B from 12 o'clock to 12 midnight using an exponential growth model, select the correct options.

Time (o'clock)	12	13	14	15	16	17	18	19	20	21	22	23	24
Quantity in A	$X$			$2X$
Quantity in B	$Y$		$2Y$		$4Y$

(1) $X > Y$ (2) At 1 PM, the quantity in A is $\frac{4}{3}X$ (3) At 3 PM, the quantity in B is $3Y$ (4) At 7 PM, the quantity in B is 1.5 times that of A (5) At 12 midnight, the quantity in B is 2 times that of A

On a coordinate plane, there is a circle with center $A(a, b)$ that is tangent to both coordinate axes. There is also a point $P(c, c)$, where $a > c > 0$, and it is known that $\overline{PA} = a + c$. Select the correct options.
(1) $a = b$ (2) Point $P$ is on the line $x + y = 0$ (3) Point $P$ is inside the circle (4) $\frac{a + c}{b - c} = \sqrt{2}$ (5) $\frac{a}{c} = 2 + 3\sqrt{2}$

On a globe with center $O$, there are five points $A$, $B$, $C$, $D$, $E$. Points $A$, $B$, $C$ are all on the equator with longitudes of East $0^{\circ}$, $60^{\circ}$, and $90^{\circ}$ respectively. Points $D$ and $E$ are both on the $30^{\circ}$ North latitude line with longitudes of East $0^{\circ}$ and $180^{\circ}$ respectively. Select the correct options.
(1) The length of the equator equals the sum of the lengths of the meridians at East $0^{\circ}$ and $180^{\circ}$ (2) The length of the $45^{\circ}$ North latitude line equals $\frac{1}{2}$ of the equator's length (3) The shortest path length from $A$ to $B$ along the equator equals the path length from $D$ to the North Pole along the East $0^{\circ}$ meridian (4) The path length from $D$ to $E$ along the $30^{\circ}$ North latitude line equals the sum of the path lengths from $D$ to the North Pole along the East $0^{\circ}$ meridian and from the North Pole to $E$ along the East $180^{\circ}$ meridian (5) The line passing through the North Pole and point $A$ is perpendicular to the line passing through the North Pole and point $C$

Two positive real numbers $a$ and $b$ satisfy $ab^{2} = 10^{5}$ and $a^{2}b = 10^{3}$. Then $\log b = \dfrac{\square}{\square}$. (Express as a fraction in lowest terms)

From the 20 integers from 1 to 20, select three distinct numbers $a$, $b$, $c$ that form an arithmetic sequence with $a < b < c$. The number of ways to choose $(a, b, c)$ is $\square\square$.

As shown in the figure, a point $P_{0}$ moves forward 2 units in a certain direction to reach point $P_{1}$, then turns left 15 degrees in the direction of motion; moves forward 2 units in the new direction to reach point $P_{2}$, then turns left 15 degrees again; moves forward 2 units in the new direction to reach point $P_{3}$, and so on.
The dot product of vectors $\overrightarrow{P_{2}P_{3}}$ and $\overrightarrow{P_{5}P_{6}}$ is $\square$. (Express as a simplified radical)

On a square piece of paper, there is a point $P$ that is 6 cm from the left edge and 8 cm from the bottom edge. Now fold the bottom-left corner $O$ of the paper inward to point $P$, as shown in the figure. The area of the folded triangle is $\square$ square centimeters.

Consider all sequences composed of only the three digits 0, 1, 2. The length $n$ of a sequence refers to the sequence consisting of $n$ digits (which may repeat). Let $a(n)$ be the total count of consecutive pairs of zeros (i.e., 00) appearing in all sequences of length $n$. For example, among sequences of length 3 containing consecutive zeros, there are 000, 001, 002, 100, 200. Among these, 000 contributes 2 occurrences of 00, and each of the others contributes 1 occurrence of 00, so $a(3) = 6$. The value of $a(5)$ is $\square$.

In an open space, there are three utility poles perpendicular to the ground with equal heights and equally spaced bases on a straight line. A person uses one-point perspective to draw these three utility poles on a canvas. A coordinate system is set up on the canvas so that the utility poles are parallel to the $y$-axis. The three base points are $A_{1}(0,0)$, $A_{2}$, $A_{3}$, all on the line $L: x + 3y = 0$; the three top points are $B_{1}(0,3)$, $B_{2}$, $B_{3}$, all on the line $M: 2x - 3y + 9 = 0$, as shown in the figure. It is known that $\overline{A_{3}B_{3}} = 2\overline{A_{1}B_{1}}$, and by one-point perspective, the intersection of lines $A_{1}B_{3}$ and $A_{3}B_{1}$ lies on line $A_{2}B_{2}$. Let $P$ be the intersection of $L$ and $M$ (this point is also called the "vanishing point").
If $\overrightarrow{PA_{1}} = k\overrightarrow{PA_{3}}$, then the value of $k$ is $\square$. (Express as a fraction in lowest terms)

In an open space, there are three utility poles perpendicular to the ground with equal heights and equally spaced bases on a straight line. A person uses one-point perspective to draw these three utility poles on a canvas. A coordinate system is set up on the canvas so that the utility poles are parallel to the $y$-axis. The three base points are $A_{1}(0,0)$, $A_{2}$, $A_{3}$, all on the line $L: x + 3y = 0$; the three top points are $B_{1}(0,3)$, $B_{2}$, $B_{3}$, all on the line $M: 2x - 3y + 9 = 0$, as shown in the figure. It is known that $\overline{A_{3}B_{3}} = 2\overline{A_{1}B_{1}}$, and by one-point perspective, the intersection of lines $A_{1}B_{3}$ and $A_{3}B_{1}$ lies on line $A_{2}B_{2}$. Let $P$ be the intersection of $L$ and $M$ (this point is also called the "vanishing point").
Find the coordinates of points $P$ and $B_{3}$.

In an open space, there are three utility poles perpendicular to the ground with equal heights and equally spaced bases on a straight line. A person uses one-point perspective to draw these three utility poles on a canvas. A coordinate system is set up on the canvas so that the utility poles are parallel to the $y$-axis. The three base points are $A_{1}(0,0)$, $A_{2}$, $A_{3}$, all on the line $L: x + 3y = 0$; the three top points are $B_{1}(0,3)$, $B_{2}$, $B_{3}$, all on the line $M: 2x - 3y + 9 = 0$, as shown in the figure. It is known that $\overline{A_{3}B_{3}} = 2\overline{A_{1}B_{1}}$, and by one-point perspective, the intersection of lines $A_{1}B_{3}$ and $A_{3}B_{1}$ lies on line $A_{2}B_{2}$. Let $P$ be the intersection of $L$ and $M$ (this point is also called the "vanishing point").
Suppose a bee stops on the middle utility pole at a position where the ratio of distances from the base to the top is $1:2$. The person wants to draw this bee on the line segment $A_{2}B_{2}$ on the canvas. Assuming the bee's position on the canvas is point $Q$, that is, the ratio of the distance from point $Q$ to the base $A_{2}$ of line segment $A_{2}B_{2}$ to the distance to the top $B_{2}$ is $1:2$, find the coordinates of point $Q$.