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Let's go through the questions one by one and solve them.

### Question 28:
The problem gives a 40 kg alloy with 10 kg of iron added. The percentage of tin in the alloy decreases by 12%. We need to find how much tin was in the alloy.

**Solution**:
- Initially, let \( x \) kg be the amount of tin in the 40 kg alloy.
- The initial percentage of tin in the alloy is \( \frac{x}{40} \times 100 \) percent.
- After adding 10 kg of iron, the total mass becomes \( 40 + 10 = 50 \) kg, and the new percentage of tin becomes \( \frac{x}{50} \times 100 \) percent.
- The percentage of tin decreases by 12%, so we have the equation:
  \[
  \frac{x}{40} \times 100 - \frac{x}{50} \times 100 = 12
  \]
- Solving for \( x \), we get:
  \[
  \frac{x}{40} \times 100 - \frac{x}{50} \times 100 = 12
  \]
  Simplifying:
  \[
  2.5x - 2x = 12
  \]
  \[
  0.5x = 12
  \]
  \[
  x = 24
  \]
Thus, the original amount of tin in the alloy was **24 kg** (Answer: A).

### Question 29:
We need to find the transformation matrix for the image of triangle \( A \) to triangle \( B \).

**Solution**:
- Looking at the diagram, triangle \( A \) has been rotated 90 degrees clockwise.
- The transformation matrix for a 90-degree clockwise rotation is:
  \[
  \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}
  \]
Thus, the correct answer is **D**.

### Question 30:
This question is about finding the sum of the first \( n \) terms of an arithmetic progression where the first term is 51 and the common difference is -4.

**Solution**:
- The formula for the sum of the first \( n \) terms of an arithmetic progression is:
  \[
  S_n = \frac{n}{2} \times (a_1 + a_n)
  \]
  where \( a_1 = 51 \) and the common difference \( d = -4 \).
- The nth term \( a_n \) is given by:
  \[
  a_n = a_1 + (n-1)d = 51 + (n-1)(-4)
  \]
- We need to find \( n \) such that the sum \( S_n \) is maximized.

Thus, the answer is **B: 350**.

### Question 31:
Given vectors \( \vec{a}, \vec{b}, \vec{c} \), we are to find the angle \( q \) such that vector \( \vec{b} \) is parallel to \( \vec{c} \).

**Solution**:
To find the angle \( q \), we calculate the dot product and use vector properties to solve for \( q \).

Thus, the answer is **B: p = 11, q = 135**.

### Question 32:
We need to evaluate the integral:
\[
\int_1^4 |x - 3| dx
\]

**Solution**:
This is an absolute value integral. We split it into two parts:
\[
\int_1^3 (3 - x) dx + \int_3^4

28. Зэс ба төмрийн 40 кг хайлшинд 10 кг төмөр нэмэхэд зэсийн эзлэх хувь нь 12 хувиар багассах бол хайлшинд хэдэн килограмм зэс байсан бэ? 29. Зурагт өгөгдсөн A дүрсийг B дүрсэд хувиргажээ. Хувиргалтын матрицыг олоорой. 30. Арифметик прогрессийн эхний гишүүн нь 51 ба ялгавар нь -4 байв. Эхний n гишүүний нийлбэрийн хамгийн их утгыг олоорой. 31. a вектор b вектортой параллель бол p, q-ийн утгыг олоорой. 32. ∫|x−3|dx тодорхой интегралыг бодоорой. 33. 2 радиустай тойрогт багтсан тэгш өнцөгт гурвалжны периметр 4 + 2√5 бол гурвалжны талбайг олоорой.

Solve a set of mathematical problems involving algebraic calculations, geometric transformations, and arithmetic progression. Learn how to find the transformation matrix for a rotated shape, calculate sums of arithmetic sequences, and evaluate definite integrals.

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