Find all the Killing vectors for the geometry with the line element: ds^2= -dt^2+e^{2t}(dr^2+r^2(d\theta ^2+\text{sin}^2\theta d\phi ^2)).

The force on a cutting tool are 2600n vertically downward and 2100 horizontal. determine the resultant force acting on the tool and the angle at which it acts.

Draw the engineering stress-strain curve for (a) bcc; (b) fcc metals and mark important points.

Aturning operation is performed with following conditions: rake angle of 12°, a feed of 0.35 mm/rev, and a depth of cut of 1.1 mm. the work piece is aluminum alloy 6061 with t6 heat treatment (a16061-t6). the resultant chip thickness was measured to be 1.0 mm. estimate the cutting force, fc. use shear stress of 207 mpa and coefficient of friction on the tool face of 0.6.