Final answer:
The question contains fragments of different math problems but lacks sufficient context or information to provide a precise answer. For double integrals involving transformations, the Jacobian determinant is typically used, but the necessary details are missing in this case.
Step-by-step explanation:
It appears that there are multiple questions and it is not clear which question needs to be answered. The phrase 'Let d = ϕ(r), where ϕ(u, v) = (u^2, u v), and r = [4, 7] × [0, 9]' suggests a transformation of regions for a double integral, but the instructions following do not provide the necessary details on how to proceed with this problem. In a typical situation, to evaluate the integral ∬∬ dy da, we would first need to understand the context of the variables and the function to be integrated. When dealing with such transformations, it's crucial to calculate the Jacobian determinant for the change of variables and then perform the integral over the transformed region. However, without further context, it is impossible to proceed with confidence. Similarly, the other parts of the question provided are fragmented and do not provide sufficient information for a complete answer. Therefore, I must refrain from providing an answer to this question.