grandes-ecoles 2013 QI.A.3

grandes-ecoles · France · centrale-maths2__pc Groups Group Homomorphisms and Isomorphisms
Verify that the map which associates to every real $t$ the matrix $R_t$ is a surjective homomorphism from the group $(\mathbb{R},+)$ onto the group $(\mathrm{SO}(2),\times)$. Is this homomorphism bijective? 
Verify that the map which associates to every real $t$ the matrix $R_t$ is a surjective homomorphism from the group $(\mathbb{R},+)$ onto the group $(\mathrm{SO}(2),\times)$. Is this homomorphism bijective?
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