The closed curve shown in the figure is described by

The magnitude of the line integral of the vector field $$F = - y\widehat i + x\widehat j$$ around the closed curve is ___________ (Round off to 2 decimal places).

A quadratic function of two variables is given as

$$f({x_1},{x_2}) = x_1^2 + 2x_2^2 + 3{x_1} + 3{x_2} + {x_1}{x_2} + 1$$

The magnitude of the maximum rate of change of the function at the point (1, 1) is ___________ (Round off to the nearest integer).

For a given vector $${[\matrix{ 1 & 2 & 3 \cr } ]^T}$$, the vector normal to the plane defined by $${w^T}x = 1$$ is

In the figure, the vectors u and v are related as : Au = v by a transformation matrix A. The correct choice of A is