What is a defining property of a rotation transformation matrix?

A rotation transformation matrix has a defining property of rotating vectors around a specified point, typically the origin in a Cartesian coordinate system. This transformation alters the angle of the vector while maintaining its magnitude. When you multiply a vector by a rotation matrix, the components of the vector are adjusted according to the specified angle of rotation, effectively 'spinning' the vector around the center point.

In contrast, the other options do not characterize rotation transformations accurately. Reflection involves flipping a vector over a line or axis, which is fundamentally different from rotation. Scaling changes a vector's length but retains its direction, which distinguishes it from rotation since the angle remains constant during scaling. Lastly, translation changes a vector's position without altering its direction or magnitude, which is not a property associated with rotation at all. Thus, the most precise description of a rotation transformation matrix is that it rotates vectors around a specified point, confirming the correctness of the answer.