(a) A two-dimensional 4-node isoparametric element is shown below in physical coordinate space (x, y) and...

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(a) A two-dimensional 4-node isoparametric element is shown below in physical coordinate space (x, y) and natural coordinate space (r, s). Determine the Jacobian matrix J, and the determinant of J, (det J), of this element. ty 2 12 cm 8 cm 2 x -2 N S 1 4 2. (b) Another two-dimensional 4-node isoparametric element is shown below in physical coordinate space (x, y) and natural coordinate space (r, s). Determine the Jacobian matrix J, and the determinant of J, (det J), of this element. The x-, y- coordinates of node i is shown as (x,y) in units of cm. (3, 4) (7,5) 2 3 (2,2) (4,2) S 1 4 2. (a) A two-dimensional 4-node isoparametric element is shown below in physical coordinate space (x, y) and natural coordinate space (r, s). Determine the Jacobian matrix J, and the determinant of J, (det J), of this element. ty 2 12 cm 8 cm 2 x -2 N S 1 4 2. (b) Another two-dimensional 4-node isoparametric element is shown below in physical coordinate space (x, y) and natural coordinate space (r, s). Determine the Jacobian matrix J, and the determinant of J, (det J), of this element. The x-, y- coordinates of node i is shown as (x,y) in units of cm. (3, 4) (7,5) 2 3 (2,2) (4,2) S 1 4 2.