grandes-ecoles 2013 QI.A.1

grandes-ecoles · France · centrale-maths2__pc Groups Symplectic and Orthogonal Group Properties
Show that $A \in \mathrm{SO}(2)$ if and only if there exists a real $t$ such that $A = R_t$ with $R_t = \left(\begin{array}{rr} \cos t & -\sin t \\ \sin t & \cos t \end{array}\right)$. 
Show that $A \in \mathrm{SO}(2)$ if and only if there exists a real $t$ such that $A = R_t$ with $R_t = \left(\begin{array}{rr} \cos t & -\sin t \\ \sin t & \cos t \end{array}\right)$.
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