Question $3$

Find ${?}^0{T}_2($in $33$ matrix form$)$ given that ${?}^0{T}_2={?}^0{T}_1^1{T}_2$ for the figure given below. Assume all frames rotate on their corresponding positive Z $-$axis $($Rot z $).$ The Point $(2\mathrm{.}5,4)$ is already given below as relative to Frame $1.$

Figure $51.$ Muliple transformations related to Problem $3.$ Source: Study Wolf $(2014)$

a$.-0\mathrm{.}5736,-0\mathrm{.}8192,1\mathrm{.}9393$

$0\mathrm{.}8192,-0\mathrm{.}5736,6\mathrm{.}5962$

$0,0,1\mathrm{.}0000$

b$.0\mathrm{.}7071-0\mathrm{.}7071,3\mathrm{.}0000$

$0\mathrm{.}70710\mathrm{.}70712\mathrm{.}0000$

c$.0\mathrm{.}1736-0\mathrm{.}9848,2\mathrm{.}5000$

$0\mathrm{.}9848,0\mathrm{.}1736,4\mathrm{.}0000$

$0,0,1\mathrm{.}0000$

d$.0\mathrm{.}7877,0\mathrm{.}6160,0\mathrm{.}9097$

$-0\mathrm{.}6160,0\mathrm{.}7877,6\mathrm{.}2285$

$0,0,1\mathrm{.}0000$