In the figure below, the black R was rotated by angle alpha around Rotocenter1 (purple). The image of that rotation (the purple R) was then rotated by angle beta around Rotocenter2 (cyan) . [list=1] [*] [i]Can a rotation of a rotation be a translation?[/i] Adjust the angles of rotation, the rotocenters, and the red vector, so that the red R coincides with the cyan R. [*] [i]What is the relationship among the angles of rotation in this case? [/i] Change the values of all three angles to confirm your conjecture. [*] [i]Can a rotation of a rotation be a 'do nothing'?[/i] Adjust the angles of rotation, the rotocenters, and the red vector, so that the cyan R coincides with the black R. [*] [i]What is the relationship among the angles of rotation when the composition is a 'do nothing'? [/i] Change the values of both angles to confirm your conjecture. [/list]