Determing the rotaion matrix for the following angle and direction
theta = 150^deg counter clockwise

To determine the rotation matrix for an angle \(\theta = 150^\circ\) counterclockwise, we can use the standard 2D rotation matrix formula for counterclockwise rotation:

\[
R(\theta) = 
\begin{bmatrix}
\cos(\theta) & -\sin(\theta) \\
\sin(\theta) & \cos(\theta)
\end{bmatrix}
\]

### Step 1: Find \(\cos(150^\circ)\) and \(\sin(150^\circ)\)
- \(\cos(150^\circ) = -\frac{\sqrt{3}}{2}\)
- \(\sin(150^\circ) = \frac{1}{2}\)

### Step 2: Plug these values into the rotation matrix:

\[
R(150^\circ) = 
\begin{bmatrix}
-\frac{\sqrt{3}}{2} & -\frac{1}{2} \\
\frac{1}{2} & -\frac{\sqrt{3}}{2}
\end{bmatrix}
\]

This is the 2D rotation matrix for a counterclockwise rotation by \(150^\circ\).

Would you like further details or clarification on the steps?

Here are 5 related questions to explore further:
1. How does the rotation matrix change for clockwise rotation?
2. What is the determinant of a 2D rotation matrix?
3. How do we apply this rotation matrix to a given vector?
4. What happens if the angle is negative?
5. How does the rotation matrix work in 3D?

**Tip:** Always remember that for a rotation matrix, the determinant is always 1, ensuring that the rotation preserves the length of vectors.

Learn how to determine the rotation matrix for a counterclockwise rotation by 150 degrees. This problem involves trigonometric concepts such as cosine and sine functions applied to a 2D rotation matrix. Suitable for high school students studying trigonometry.

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