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Let's take a look at each of the problems on this page and break them down.

### Câu 1:
This problem asks about a cube containing a square pyramid (a solid toy) inside. The square pyramid has its base coincident with one face of the cube, and its apex touching the opposite face. The side length of the cube is \(0.4m\). You need to calculate the volume of the space inside the cube that is **not** occupied by the pyramid, and express it as a percentage.

To solve:
- The volume of the cube is \( V_{\text{cube}} = a^3 \), where \( a = 0.4m \).
- The volume of the pyramid is \( V_{\text{pyramid}} = \frac{1}{3} A_{\text{base}} h \), where the base area \( A_{\text{base}} \) is the area of one face of the cube, and \( h \) is the height (which is the side length of the cube, \( 0.4m \)).

You then subtract the volume of the pyramid from the volume of the cube to get the empty space, and find its percentage of the total cube volume.

### Câu 2:
This is about a sequence \( (u_n) \) where the general term is given as:
\[
u_n = \frac{2n - 1}{3n + 2}
\]
You are asked to find the position of the term \( \frac{459}{692} \) in this sequence. Essentially, you need to solve:
\[
\frac{2n - 1}{3n + 2} = \frac{459}{692}
\]
This requires solving for \( n \).

### Câu 3:
In this problem, you are asked to determine the total number of seats in a hall with 30 rows. The first row has 15 seats, and each subsequent row has 3 more seats than the previous row. This describes an arithmetic sequence where:
- First term \( a_1 = 15 \),
- Common difference \( d = 3 \),
- Number of rows \( n = 30 \).

You can calculate the total number of seats by summing the sequence using the formula for the sum of an arithmetic sequence:
\[
S_n = \frac{n}{2} \left(2a_1 + (n-1)d\right)
\]

### Câu 4:
You are given a function \( f(x) = (x^2 - 1)(x - 4) \) and are asked to find the number of local maxima (critical points) for the related function \( y = f(3 - x) \). To solve this, you first find the derivative of \( f(x) \), set it equal to zero to find the critical points, and then substitute into \( y = f(3 - x) \) to analyze how these critical points behave in the transformed function.

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Would you like a detailed step-by-step explanation of any particular question? Also, here are 5 related questions for further practice:

1. How do you find the critical points of a cubic polynomial function?
2. Can you calculate the volume of a cone inside a cube with known side lengths?
3. How do you generalize the formula for the sum of any arithmetic sequence?
4. What is the derivative of a product of polynomials using the product rule?
5. How do you solve a rational equation involving unknowns in both the numerator and denominator?

**Tip:** When solving rational equations, always ensure the denominator is non-zero, as this will help you avoid invalid solutions.

The problems include geometry (volume of a cube and pyramid), sequences, arithmetic series (sum of rows of chairs), and calculus (finding critical points).

Solve geometry problems involving the volume of a cube and a square pyramid, find the sum of an arithmetic sequence for rows of chairs, and analyze critical points of polynomial functions using derivatives. Suitable for high school students.

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