Problem: A metal plate whose temperature at the point (x,y) is given T(x,y)=200−5x2−3xy−y2. Given a...

Problem: A metal plate whose temperature at the point (x,y) is given ${\displaystyle T(x,y)=200-5x^2-3xy-y^2}$. Given a function f(x,y), the vector ${\displaystyle \mathrm{\nabla }f=<f_x,f_y>}$ points in the direction of greatest increase for f.
Problem 1: Compute ${\displaystyle \mathrm{\nabla }T(x,y)}$
Question 1: $\mathrm{\nabla }$$T(x,y)=<-10x-3y,-3x-2y>$. Is it right?
Problem 2: Denote the position at time t by ${\displaystyle r\left(t\right)=(x\left(t\right),y\left(t\right))}$. We want ${\displaystyle r^{\prime }\left(t\right)=\mathrm{\nabla }T\left(r\left(t\right)\right)}$ for all t to ensure the temperature is increasing as much as possible. Interpret this equation as a system of linear ODEs with the form ${\displaystyle r^{\prime }=Ar}$
Question 2: not sure how to proceed.