## Recent **Performance Management** Questions & Answers

###### Use Example 10.3.6 to find an appropriate subset of GL3.R/ with which to identify
Isom2.R/, and then check that the correspondence is an isomorphism b...

##### Use Example 10.3.6 to find an appropriate subset of GL3.R/ with which to identify
Isom2.R/, and then check that the correspondence is an isomorphism by using the
formula in Exercise 2 above.
Note: This gives another way to see that Isom2.R/ ...

###### Show that Isom2.R/=T2 ...

##### Show that Isom2.R/=T2 ...

###### If f is an isometry, show that f takes lines to lines, and takes any triangle to a
congruent triangle....

##### If f is an isometry, show that f takes lines to lines, and takes any triangle to a
congruent triangle....

###### Show that if f D P A 2 Isom2.R/, then f 1 D AT .P /AT ....

##### Show that if f D P A 2 Isom2.R/, then f 1 D AT .P /AT ....

###### Show that if f D P A and g D QB belong to Isom2.R/, then fg D .AQCP /AB....

##### Show that if f D P A and g D QB belong to Isom2.R/, then fg D .AQCP /AB....

###### Prove each of the statements in Example 10.6.1....

##### Prove each of the statements in Example 10.6.1....

###### Let K be the subgroup 1 0 0 ?1 of O2.R/ generated by the reflection about
the x-axis. Show that O2.R/ is the internal semidirect product of SO2....

##### Let K be the subgroup 1 0 0 ?1 of O2.R/ generated by the reflection about
the x-axis. Show that O2.R/ is the internal semidirect product of SO2.R/ by K....

###### Prove that all elements A 2 O2.R/ preserve norms and distances....

##### Prove that all elements A 2 O2.R/ preserve norms and distances....

###### Prove that all elements A 2 O2.R/ preserve inner products....

##### Prove that all elements A 2 O2.R/ preserve inner products....