1. Prove that we can transform a segment by transforming its endpoints and then constructing a...

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1. Prove that we can transform a segment by transforming its endpoints and then constructing a new segment with the transformed end points. 2. Prove that two successive 2D rotations are additive: R(0₁)R(^2) = R(a1 + a2), where R(a) denotes a 2x2 rotation matrix of rotation angle a. (Recall that sin(a₁ + a₂) = sin α₁ cos a₂ + cosa₁ sin a2, and cos(a₁ + a₂) = cos a co 2 sin α₁ sin α₂.) 1. Prove that we can transform a segment by transforming its endpoints and then constructing a new segment with the transformed end points. 2. Prove that two successive 2D rotations are additive: R(0₁)R(^2) = R(a1 + a2), where R(a) denotes a 2x2 rotation matrix of rotation angle a. (Recall that sin(a₁ + a₂) = sin α₁ cos a₂ + cosa₁ sin a2, and cos(a₁ + a₂) = cos a co 2 sin α₁ sin α₂.)