(Solved): The temperature of a plate is described by scalar field T(x,y)=5+2x2+y2. Find the direction that a ...

The temperature of a plate is described by scalar field $T(x,y)=5+2x^2+y^2$. Find the direction that a fly should take from point $\mathrm{P}(4,2)$ to cool off as rapidly as possible. Question 4 A flow field is described by $\mathbf{F}=(yz\ln x)\mathbf{i}+(2x-3yz)\mathbf{j}+\left(x{y}^2{z}^3\right)\mathbf{k}$. a) Comment on the compressibility of the flow. Show your calculation b) Determine whether the flow is rotational or irrotational. Show your calculation