6. (4 points) now, suppose the air temperature is constant (t) = 0, Vt but the fan speed is variable, thereby changing the velocity v(t) [m/s] at which the air is blown across the GPU. Jan input v mis cool air input JIS fan GPU output Figure 2: GPU cooling. two inputs: (1) the heat generated by the computations, q(t), and (2) the velocity of the air blown across it, v(t), determined by the fan speed. both inputs affect one output: the temperature of the GPU, 0(t). a (nonlinear) dynamic model for the output (t) in response to the two inputs q(t) and v(t) accounts for the change in the heat transfer coefficient when v changes: = qt) + (U. + b[v(t)]2) Aa 0(t)]. (4) dt here, C, Uo, b, and A are [constant] parameters. let v, , and 7 be nominal steady state values of v(t), q(t), and e(t), respectively. write a linearized model about these nominal steady state values. your model should be written in terms of the deviation variables: v*(t):=v(t) - q*(t) := 9(t) - 9 * (t):= 0(t)-0