csat-suneung 2012 Q10

csat-suneung · South-Korea · csat__math-science 3 marks Linear transformations

On the coordinate plane, a rotation transformation $f$ centered at the origin maps the point $( 1,0 )$ to a point $\left( \frac { \sqrt { 3 } } { 2 } , a \right)$ in the first quadrant. When the sum of all components of the matrix representing the rotation transformation $f$ is $b$, what is the value of $a ^ { 2 } + b ^ { 2 }$? [3 points]
(1) $\frac { 31 } { 12 }$
(2) $\frac { 11 } { 4 }$
(3) $\frac { 35 } { 12 }$
(4) $\frac { 37 } { 12 }$
(5) $\frac { 13 } { 4 }$

On the coordinate plane, a rotation transformation $f$ centered at the origin maps the point $( 1,0 )$ to a point $\left( \frac { \sqrt { 3 } } { 2 } , a \right)$ in the first quadrant.\\
When the sum of all components of the matrix representing the rotation transformation $f$ is $b$, what is the value of $a ^ { 2 } + b ^ { 2 }$? [3 points]\\
(1) $\frac { 31 } { 12 }$\\
(2) $\frac { 11 } { 4 }$\\
(3) $\frac { 35 } { 12 }$\\
(4) $\frac { 37 } { 12 }$\\
(5) $\frac { 13 } { 4 }$

Paper Questions

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