# Räumliche Drehung/z-Achse/45 Grad/Bzgl. (1,2,4), (3,3,-1), (5,0,7)/Aufgabe/en

Zur Navigation springen Zur Suche springen

Let

${\displaystyle \varphi \colon \mathbb {R} ^{3}\longrightarrow \mathbb {R} ^{3}}$

be the space rotation by ${\displaystyle {}45}$ degree around the ${\displaystyle {}z}$-axis counterclockwise. How does the matrix describing ${\displaystyle {}\varphi }$ with respect to the basis

${\displaystyle {\begin{pmatrix}1\\2\\4\end{pmatrix}},\,{\begin{pmatrix}3\\3\\-1\end{pmatrix}},\,{\begin{pmatrix}5\\0\\7\end{pmatrix}}}$

look like?