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With reference to the conventional Cartesian (x, y) coordinate system, the vertices of a triangle have the following coordinates; (x<sub>1</sub>, y<sub>1</sub>) = (1, 0);(x<sub>2</sub>, y<sub>2</sub>) = (2, 2); (x<sub>3</sub>, y<sub>3</sub>) = (4, 3). The area of the triangle is equal to

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Describe the equation of the circular orbit in cartesian coordinates. Given, a point is P(6,054.78,6492.95) along the orbit in cartesian coordinates. Assume the centre of larger body to be the origin O(0,0).

Convert the (10, 90, 60) coordinates to Cartesian coordinates which are in Spherical coordinates.

The Cartesian coordinates can be related to cylindrical coordinates and spherical coordinates. State True/False.

If coordinates of vertices of a triangle are (7, 6, 4), (5, 4, 6), (9, 5, 8), find the coordinates of centroid of the triangle.

An undirected graph has 8 vertices labelled 1, 2, …,8 and 31 edges. Vertices 1, 3, 5, 7 have degree 8 and vertices 2, 4, 6, 8 have degree 7. What is the degree of vertex 8?

The relation between the stress component in x-direction on a horizontal plane in Cartesian coordinates and polar coordinates for vertical line load is ___________

The relation between the stress component in z-direction on a horizontal plane in Cartesian coordinates and polar coordinates for vertical line load is ___________

The relation between the shear stress component in xz-plane in Cartesian coordinates and polar coordinates for vertical line load is ___________

Select differences between reference type and value type: i. Memory allocated to ‘Value type’ is from heap and reference type is from ‘System. ValueType’ ii. Memory allocated to ‘Value type’ is from ‘System. ValueType’ and reference type is from ‘Heap’ iii. Structures, enumerated types derived from ‘System. ValueType’ are created on stack, hence known as ValueType and all ‘classes’ are reference type because values are stored on heap

Let Z be the set of real integers and R the set of real numbers. The sampling process may be viewed as partitioning the x-y plane into a grid, with the central coordinates of each grid being from the Cartesian product Z2, that is a set of all ordered pairs (zi, zj), with zi and zj being integers from Z. Then, f(x, y) is a digital image if (x, y) are integers from Z2 and f is a function that assigns a gray-level value (that is, a real number from the set R) to each distinct coordinate pair (x, y). What happens to the digital image if the gray levels also are integers?