The symbols you provided, like 1 R, 2 R O, and 2 R 1, appear to represent operations involving rotation matrices or transformations. Without additional context, I'll provide a general interpretation related to rotations and matrices.

1. 1 R:

   • If this refers to a rotation matrix, R could represent a standard rotation matrix.
   • The number "1" could represent a 1-degree rotation (or a 1-radian rotation if the context is in radians).
   • In general, a 2D rotation matrix for a counterclockwise rotation by an angle $\theta$ is: \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix}$$ For **1-degree rotation**, substitute $$\theta = 1^\circ$$ in the matrix.

2. 2 R O:

   • This may involve a rotation (R) and possibly a point (O) or an origin.
   • If O represents the origin, then 2 R O might represent a rotation of 2 degrees around the origin.
   • If it's a 2D rotation, the same rotation matrix formula would apply, but with $\theta = 2^\circ$.

3. 2 R 1:

   • If 2 R 1 involves rotations as well, it could mean a rotation of 2 degrees or 2 radians, followed by another transformation or operation (possibly related to the number 1).
   • If it's another 2D rotation, plug in the appropriate angle (either 2 radians or 2 degrees depending on context).

General Approach to Rotation:

• If you’re rotating a point $P(x, y)$ by an angle $\theta$, you apply the rotation matrix $R(\theta)$ to the point. The new coordinates $P'(x', y')$ are given by: x' \\ y' \end{bmatrix} = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}$$ - The result gives the new coordinates after rotation.

If the symbols stand for something else (e.g., abstract algebra or group theory), feel free to clarify the context!

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Would you like a detailed calculation using a specific rotation matrix? Let me know!

Here are 5 related questions:

1. What context is this problem from (geometry, physics, etc.)?
2. Are the numbers in 1 R, 2 R O degrees or radians?
3. Does O represent a point like the origin?
4. Are these transformations taking place in 2D or 3D space?
5. Are there any specific vectors or points to rotate?

Tip: Always clarify the unit of angles (degrees or radians) when working with rotation matrices to avoid errors.