Match the linear transformation matrices listed in the first column to their interpretations in the second column.

Each axis of $$NC$$ machine is driven by a stepper motor drive with a lead screw. The pitch of lead screw is $$p$$ $$mm.$$ The step angle of stepper motor per pulse input is $$\alpha $$ degrees/pulse. The ratio of gear drive in stepper motor drive is $$g$$(number of turns of the motor for each single turn of the lead screw). The number of pulses required to achieve a linear movement of $$x$$ $$mm$$ is

A $$CNC$$ instruction $$G91\,\,\,G01\,\,\,X30\,\,\,Y40\,\,\,F100$$ commands the movement of tool along the path at a feed rate of $$100mm/min$$ $$(G91$$-incremental format and $$G01$$-linear interpolation). The feed rate of the tool (in $$mm/min)$$ along the $$X$$ axis will be _______________

In a $$CAD$$ package, mirror image of a $$2D$$ points $$P(5, 10)$$ is to be obtained about a line which passes through the origin and makes an angle of $${45^ \circ }$$ counterclockwise with the $$X$$-axis. The coordinates of the transformed points will be