What is the derivative of sin(x)?
The derivative of sin(x) with respect to x is cos(x), a fundamental result in calculus.
Which matrix operation results in a change in the determinant's sign?
Swapping two rows of a matrix changes the sign of its determinant.
What is the Laplace transform of 1?
The Laplace transform of a constant 1 is 1/s.
If A is an invertible matrix, what is the determinant of A inverse?
The determinant of the inverse of a matrix A is the reciprocal of the determinant of A.
Which of the following is a second-order differential equation?
A second-order differential equation involves the second derivative of a function.
What is the probability of getting a sum of 7 when two dice are thrown?
There are 6 combinations that give a sum of 7 out of 36 possible outcomes, resulting in a probability of 1/6.
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Which numerical method is used for solving ordinary differential equations?
The Runge-Kutta method is a popular iterative technique to approximate solutions to ODEs.
What is the general solution of a homogeneous linear differential equation?
The general solution is the sum of the complementary function and a particular integral.
In probability, what does a cumulative distribution function (CDF) represent?
The CDF gives the probability that a random variable is less than or equal to a certain value.