Using Python, Triangle A has vertices at (-1,0), (1, 0), and (0, 1). Triangle B has vertices at (0, 0), (0, 6), and (3, 3) on a standard x - y coordinate system with +x pointing to the right and +y pointing up. 1. Use the cross product to calculate the area of each triangle.

Using python or matlab to compute this.

Write the python syntax for centered differences of all interior points of a 1D field F, and forward and backward differences on the boundaries. Use vectorized notation and assume that the grid spacing is dx

Write the 2D rotation matrix that rotates by 90 degrees clockwise.

PYTHON/JUPYTER NOTEBOOKS Given the following net reaction rate density vector in units of mols/(s ml) r =(0.690351.11066−0.13213−0.886660.13489−0.50093−0.54989). Compute the species production rate density vector, r, and kindly  show the results with 5 decimal places and state the units. Explain how you obtained the result and what it means.