Ex10 7

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 10.7}$

Give a geometric interpretation for $R(\theta)$ and $T(\phi)$ of Section 5.4.1 by determining their behavior on the set of mixed states viewed as points of the Bloch sphere.