grandes-ecoles 2013 QI.A.4

grandes-ecoles · France · centrale-maths2__pc Groups Group Homomorphisms and Isomorphisms
Show that, for all $t$ in $\mathbb{R}$ and all non-zero $u$ in $\mathbb{R}^2$, $t$ is a measure of the oriented angle $(u\widehat{\rho_t(u)})$, where $\rho_t$ is the endomorphism (the rotation of angle $t$) $f_{R_t}$ canonically associated with $R_t$. 
Show that, for all $t$ in $\mathbb{R}$ and all non-zero $u$ in $\mathbb{R}^2$, $t$ is a measure of the oriented angle $(u\widehat{\rho_t(u)})$, where $\rho_t$ is the endomorphism (the rotation of angle $t$) $f_{R_t}$ canonically associated with $R_t$.
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.B.1 QI.B.2 QI.C.1 QI.C.2 QI.C.3 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.B.1 QII.B.2 QII.B.3 QIII.A.1 QIII.A.2 QIII.A.3 QIII.B.1 QIII.B.2 QIII.B.3 QIII.C QIII.D.1 QIII.D.2 QIII.D.3 QIII.E.1 QIII.E.2 QIII.E.3 QIII.E.4 QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.A.5 QIV.A.6 QIV.B.1 QIV.B.2 QIV.B.3 QIV.B.4 QIV.B.5 QIV.C.1 QIV.C.2 QIV.C.3 QIV.D.1 QIV.D.2 QV.A.1 QV.A.2 QV.B.1 QV.B.2 QV.C.1 QV.C.2