construction de l'image réelle ou virtuelle d'un objet plan par une lentille mince convergente

prise de mesures algébriques

Cofactors Determinant and inverse of a 3x3 matrix.

Applied calculation broken down in core calculation steps.

Applied calculation broken down in core calculation steps.

Applied calculation broken down in core calculation steps.

Find the determinant and inverse of a $2 \times 2$ invertible matrix.

Exercises on calculating the determinant of 2x2 and 3x3 matrices.

Multiplication of two matrices.

3-part question with drop-downs testing understanding of when matrices are conformable.

Multiply 2 random 2x2 matrices

Single part question with 2x2 matrix multiplied by a small integer.

Identify elements by their subscript notation from given matrices.

Classifying matrices (dimensions/order) (5 parts).

The general solution to an ODE is given.  The student must deduce from its form that the characteristic equation has a repeated root and find the coefficients in the original ODE.

The general solution to an ODE is given.  The student must deduce from its form that the characteristic equation has complex roots and find the coefficients in the original ODE.

This questions gives a bipartite graph and asks students to identify a full matching of the graph, if it exists.

An ODE is displayed (in standard form).  Choices are presented to classify the ODE: fist/second order, linear/nonlinear, homogeneous/nonhomogeneous.

Solve a system of linear equations using Gaussian elimination.

Use the pythagorean hyperbolic identity aftre a substitution to exaluate an integral (1 part).

Select a matrix from a list of 4 that makes the trandformation shown in a randomly chosen (from 4) diagram.

Matching exercise with terminology: zero, square, diagonal, identity, upper/lower triangular

Tests understanding of order and subscript notation for matrices (three parts)

Use defintions of the hyperbolic functions to integrate by considering exponentials.

Rearrange and make a substitution to integrate a quotient to a function in terms of arsinh.

Rearrange and make a substitution to integrate a quotient to a function in terms of arsinh.

Use double angle an pythagorean identities to manipulate before integrating.