The question asks which of the given rotations will map the polygon onto itself. The polygon shown is a square, as indicated by its four equal sides and right angles.

For a square, rotations that map it onto itself (known as symmetries) must be multiples of $90^\circ$ because it has four symmetrical positions (0°, 90°, 180°, and 270°).

Let's examine each option:

1. Rotation of 45° clockwise: This does not map the square onto itself, as 45° is not a multiple of 90°.
2. Rotation of 90° counterclockwise: This does map the square onto itself because 90° is one of the symmetrical rotations.
3. Rotation of 120° counterclockwise: This does not map the square onto itself, as 120° is not a multiple of 90°.
4. Rotation of 30° counterclockwise: This does not map the square onto itself, as 30° is not a multiple of 90°.

So, only the 90° rotation (option 2) will carry the square onto itself.

Would you like a more detailed explanation or have any questions?

Here are some additional related questions to explore:

1. What are the rotational symmetries of other regular polygons, like a hexagon?
2. How can we identify the angle of rotation symmetry for any regular polygon?
3. What other types of transformations can map a square onto itself?
4. What is the relationship between the number of sides of a regular polygon and its angle of rotation symmetry?
5. How do rotational and reflectional symmetries differ in polygons?

Tip: For a regular polygon with $n$ sides, the smallest angle of rotation symmetry is $\frac{360^\circ}{n}$.