Let G be the additive group of real numbers. Let the action of θ ∈ G on the real plane ℝ2 be given by rotating the plane counterclockwise about the origin through θ radians. Let P be a point other than the origin in the plane.
a. Show ℝ2 is a G-sel.
b. Describe geometrically the orbit containing P.
c. Find the group Gp.
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