Question about the sign of the shearing deformation terms
Did you try to sketch one of those situations? Try a square grid, define x and y, and then put $U$ and $V$ components onto one of the grid points, which you choose as starting point.  

Now proceed to implement a). For example, from your starting arrows, go to the next grid point eastwards, and implement $\frac{dV}{dx}&lt;0$, i.e. the upwards pointing arrows become smaller as you go eastwards. Do the same for U. Repeat for enough grid points until you see a pattern. Now connect $U$ and $V$ components into the final, two-dimensional velocity vector $\vec v$.

In this way you will possibly self-answer your question. I don't know if I can help you more, because I don't know what you mean with \


  I would like to know what does it mean to have


The end result will be the graphical representation of a vector field. The shear tensor simply measure the amount of shear in each vector field. You will discover that some field structures surprisingly possess shear, while others don't.