Given a R2 point defined on the canonical x,y axis, i⃗ =(22), what are the coordinates in a new coordinate system with the origin at j⃗ =(11), and axes at 45 degrees? (The rotated first axis will be aligned to (11) in an unrotated coordinate system, with an origin at j⃗ ). Denote this changed vector as k⃗ Enter your answers as numbers.kx=?______ ky=?______

A. Scaled followed by Translation followed by Rotation
B. Rotation followed by Scale followed by Translation
C. Translation followed by Rotation
D. Rotation followed by Translation
E. None of the above.

A. \( R(\vec{a},\theta) \)
B. \( R(\vec{a},-\theta) \)
C. \( -R(\vec{a},\theta)\)
D. \( -R(-\vec{a},\theta)\)
E. The result is unpredictable.
F. None of the above.

A. \( R(-\vec{a},\theta) = R(\vec{a},\theta) \)
B. \( R(-\vec{a},\theta) = R(\vec{a},\theta+\pi) \)
C. \( R(-\vec{a},\theta) = -R(\vec{a},\theta) \)
D. \( R(-\vec{a},\theta) = R(\vec{a},-\theta) \)
E. The result is unpredictable.
F. None of the above.