- What is the name of the subgroup of the affine plane group generated by the transformations of the form $$ x \mapsto a \begin{pmatrix} \cos\theta & -\sin\theta\\ \sin\theta &\cos\theta \end{pmatrix} x+b, $$ $a \in \mathbb{R},$ and $ x,b \in \mathbb{R}^2?$
- What is relations between the group and its subgroups of rotations, translations and scaling? For example is the group the direct or semidirect product of such subgroups?
2026-03-31 11:19:35.1774955975
What is the name of the group?
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