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Let's address each of the mathematical questions one by one based on the image you've uploaded:

### Câu 1:
This question describes a square-based pyramid (hình chóp tứ giác đều) placed inside a cube. The top vertex of the pyramid coincides with one corner of the cube, while its base aligns with one face of the cube. Given the cube's side length of 0.4 meters, the problem asks for the volume of the space inside the cube not occupied by the pyramid.

**Solution Strategy**:
1. **Cube's volume**: The volume of the cube is given by \( V_{\text{cube}} = a^3 \), where \( a = 0.4 \) meters is the side length.
2. **Pyramid's volume**: The volume of a pyramid with a square base and height equal to the side length of the cube can be computed as \( V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \).
   - The base area is \( a^2 \).
   - The height is the side length of the cube \( a = 0.4 \).

Finally, subtract the volume of the pyramid from the volume of the cube to get the desired volume.

### Câu 2:
The sequence \((u_n)\) is defined by \( u_n = \frac{2n-1}{3n+2} \). You are asked to find the term corresponding to the fraction \( \frac{459}{692} \).

**Solution Strategy**:
We can solve this equation by setting \( \frac{2n-1}{3n+2} = \frac{459}{692} \), and then solve for \( n \). This will involve cross-multiplying and simplifying to find the value of \( n \).

### Câu 3:
This problem describes an arrangement of seats in a room with 30 rows. The first row has 15 seats, and each subsequent row has 3 more seats than the previous one. The question asks for the total number of seats in the room.

**Solution Strategy**:
This describes an arithmetic progression where:
- The first term \( a_1 = 15 \),
- The common difference \( d = 3 \),
- The number of rows (terms) \( n = 30 \).

Use the sum formula for an arithmetic sequence:
\[
S_n = \frac{n}{2} \times [2a_1 + (n-1)d]
\]
Substitute the known values to find the total number of seats.

### Câu 4:
The given function is \( f(x) = (x^2 - 1)(x - 4) \), and you are asked to determine how many local extrema \( y = f(3-x) \) has.

**Solution Strategy**:
1. **Find the derivative of \( f(x) = (x^2 - 1)(x - 4) \)** using the product rule.
2. Solve for the critical points by setting \( f'(x) = 0 \).
3. Analyze the critical points to determine where local maxima or minima occur.
4. Transform the result for \( y = f(3 - x) \), which reflects the function, and see how it affects the critical points and the number of extrema.

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### 5 Related Questions:
1. How do you compute the volume of irregular geometric shapes?
2. What is the method to solve for terms in a sequence using a given term formula?
3. How can you apply the sum of an arithmetic progression to other real-life situations?
4. What are the steps to analyze critical points in a function for local maxima and minima?
5. How do reflections of functions affect their critical points and extrema?

### Tip:
For calculus problems, always confirm the behavior of the function around critical points by using the second derivative test or analyzing changes in the sign of the first derivative.

Câu 1: Một cái hộp hình lập phương, bên trong nó dựng một mô hình đồ chơi có dạng hình chóp tứ giác đều ... Câu 2: Cho dãy số (u_n) có số hạng tổng quát u_n = (2n-1)/(3n+2)... Câu 3: Trong một khán phòng có tất cả 30 dãy ghế, dãy đầu tiên có 15 ghế... Câu 4: Cho hàm số y = f(x) có đạo hàm f'(x)...

Learn how to solve geometry problems involving cubes and pyramids, sequences, and calculus with derivatives. This page offers detailed solutions to questions about calculating volumes, finding terms in arithmetic sequences, and analyzing critical points in functions.

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