## Decode Rotation Matrix

Enter the elements of the 2×2 rotation matrix:

**Introduction:**

Decode a Rotation Matrix tool allows you to input the elements of a 2×2 rotation matrix and deciphers the angle of rotation it represents.

**Matrix Input:**

- You can input the elements of the rotation matrix in the provided table. The default values represent the identity matrix, which indicates no rotation.
- Each cell in the table corresponds to an element of the rotation matrix.

**Decode Rotation Matrix:**

- Clicking the “Decode Rotation Matrix” button calculates the angle of rotation based on the provided matrix elements.
- The calculated angle of rotation is displayed below the button.

**Benefits of Using This Tool:**

**Quick Deciphering:**Easily determine the angle of rotation encoded in a given 2×2 rotation matrix.**Accuracy:**Precisely calculates the angle of rotation using the matrix elements.**Educational:**Helps understand the relationship between rotation matrices and angles of rotation.

**FAQ:**

**Q: What is a rotation matrix?** A: A rotation matrix is a square matrix used to perform rotations in the plane. It represents a transformation that rotates points in the plane around the origin.

**Q: How does the tool calculate the angle of rotation?** A: The tool uses the elements of the rotation matrix to calculate the angle of rotation using trigonometric functions.

**Q: What does the identity matrix represent in terms of rotation?** A: The identity matrix represents no rotation. The default values in the input table correspond to the identity matrix.

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