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

For a $$3$$-axes $$CNC$$ table, the slide along the vertical axis of the table driven by a $$DC$$ servo motor via lead screw nut mechanism. The lead screw has a pitch of $$5mm.$$ This lead screw is fitted with a relative (incremental) circular encoder. The basic length unit $$(BLU)$$ of the slide along the vertical axis of the table is $$0.005mm.$$ When the table moves along the vertical axis by $$9mm.$$ The corresponding number of pulses generated by the encounter is

The total angular movement (in degrees) of a lead screw with a pitch of $$5.0mm$$ to drive the work table by a distance of $$200mm$$ in a $$NC$$ machine is

A titanium sheet of $$5.0mm$$ thickness is cut by wire cut $$EDM$$ process using a wire of $$1.0mm$$ diameter. A uniform spark gap of $$0.5mm$$ on both sides of the wire is maintained during cutting operation. If the feed rate of the wire into the sheet is $$20mm/min,$$ the material removal rate (in $$m{m^3}/\min $$) will be