Among the following, a rational number is:

$10x = 6.\overline{6}$.

The correct option is (D).
$\boxed{\text{D}}$

3. The degree of the polynomial $5x^7 + 2x - 4x + 10$ is:
The degree of a polynomial is the highest exponent of the variable in the polynomial.

The terms are $5x^7$, $2x^1$, $-4x^1$, and 10 (which is $10x^0$).

The correct option is (D).
$\boxed{\text{D}}$

4. The zero of the polynomial $p(x) = -7x + 7$ is:
The zero of a polynomial is the value of $x$ for which $p(x) = 0$.

The correct option is (D).
$\boxed{\text{D}}$

5. The coordinates of origin are:
The origin is the point where the x-axis and y-axis intersect in a Cartesian coordinate system.
The coordinates of the origin are $(0,0)$.

The correct option is (C).
$\boxed{\text{C}}$

6. The number of dimensions a point has is:
A point is a fundamental concept in geometry that represents a specific location. It has no length, width, or height.
Therefore, a point has 0 dimensions.

The correct option is (A).
$\boxed{\text{A}}$

7. The non-acute angle among the following is:
An acute angle is an angle that measures less than $90^\circ$. A non-acute angle is an angle that measures $90^\circ$ or greater.

• (A) $125^\circ$: This is greater than $90^\circ$, so it is an obtuse angle and thus non-acute.
• (B) $95^\circ$: This is greater than $90^\circ$, so it is an obtuse angle and thus non-acute.
• (C) $0^\circ$: This is a zero angle, which is not non-acute in the context of being $\ge 90^\circ$.
• (D) $75^\circ$: This is less than $90^\circ$, so it is an acute angle.

Both (A) and (B) are non-acute angles. Assuming the question expects a single answer, we select the first valid option.

The correct option is (A).
$\boxed{\text{A}}$

8. In the given figure, a pair of vertically opposite angles is:
Vertically opposite angles are formed when two lines intersect. They are the angles opposite each other at the intersection point.
From the figure, lines AC and BD intersect at O.
The pairs of vertically opposite angles are $\angle AOC$ and $\angle BOD$ (or $\angle DOB$), and $\angle AOD$ and $\angle BOC$.

• (A) $\angle AOC$ and $\angle DOB$: This is a pair of vertically opposite angles.
• (B) $\angle AOC$ and $\angle AOB$: These are adjacent angles forming a linear pair.
• (C) $\angle AOD$ and $\angle AOC$: These are adjacent angles forming a linear pair.
• (D) $\angle DOB$ and $\angle BOC$: These are adjacent angles forming a linear pair.

The correct option is (A).
$\boxed{\text{A}}$

SECTION II: VERY SHORT ANSWER QUESTIONS

1. Simplify: $(3+\sqrt{3})(2+\sqrt{2})$

The expression cannot be simplified further as the square root terms are different.

2. What are binomials? Give an example.
A binomial is a polynomial that consists of exactly two terms. These terms are typically separated by an addition or subtraction sign.
Example: $\boxed{x+y}$ (Other examples include $2x^2 - 5$, $3a + 7b$, etc.)

3. Find the value of $p(x) = 5x^3 - 3x + 7$ when $x = 1$.

The value of $p(x)$ when $x=1$ is $\boxed{9}$.

4. Name the part of a line which has two endpoints.
The part of a line which has two endpoints is called a $\boxed{\text{line segment}}$.

5. Define parallel lines.
Parallel lines are two distinct lines in a plane that $\boxed{\text{never intersect}}$ and maintain a constant distance from each other.

6. Define an obtuse angle.
An obtuse angle is an angle that measures $\boxed{\text{greater than } 90^\circ \text{ but less than } 180^\circ}$.

7. If one angle of a linear pair is $75^\circ$, find the other angle.

The sum of angles in a linear pair is $180^\circ$.

The other angle is $\boxed{105^\circ}$.

8. If $l \parallel m$ and $m \parallel n$, what is your conclusion about lines $l$ and $n$?
If line $l$ is parallel to line $m$, and line $m$ is parallel to line $n$, then by the transitive property of parallel lines, $\boxed{\text{line } l \text{ is parallel to line } n}$.