Any ellipse can be obtained by rotation and translation of a canonical ellipse with the proper semi-diameters.

Any transversal section of a plane perpendicular to this axis has to behave as a two dimensional rotation.

Any rotation in three-dimensions can be represented as an axis vector and an angle of rotation.

Any rotation in three dimensions can be described by a rotation by some angle about some axis.

Any of the shafts can be used to input rotation, and the other ( s ) to output it.

* Any reflection, translation and rotation is a global isometry on Euclidean spaces.

Any probability distribution which obeys a condition on correlation functions called reflection positivity lead to a local quantum field theory after Wick rotation to Minkowski spacetime.

Any transformation of the plane leaving this pattern invariant can be decomposed into a translation, ( x, y ) → ( n + x, y ), optionally followed by a reflection in either the horizontal axis, ( x, y ) → ( x ,− y ), or the vertical axis, ( x, y ) → (− x, y ), provided that this axis is chosen through or midway between two dots, or a rotation by 180 °, ( x, y ) → (− x ,− y ) ( ditto ).

Any rotation can be legitimately described both ways, as vectors and coordinate systems actually rotate with respect to each other.

Any two mirrors with the same fixed point and same angle give the same rotation, so long as they are used in the correct order.

Any rotation preserves distances on the surface of the ball.

* Any ring of matrices with coefficients in a commutative ring R forms an R-algebra under matrix addition and multiplication.

Any linear combination of the column vectors of a matrix A can be written as the product of A with a column vector:

Any n × n permutation matrix can be constructed as a product of no more than n − 1 transpositions.

Any orthogonal matrix of size n × n can be constructed as a product of at most n such reflections.

* Any square matrix with unit Euclidean norm is the average of two unitary matrices.

Any invertible matrix can be uniquely represented according to the polar decomposition as the product of a unitary matrix and a hermitian matrix with positive eigenvalues.

Any n × n matrix A of the form

To show that U ( n ) is connected, recall that any unitary matrix A can be diagonalized by another unitary matrix S. Any diagonal unitary matrix must have complex numbers of absolute value 1 on the main diagonal.

Any square diagonal matrix is also a symmetric matrix.

Any square matrix can be viewed as the adjacency matrix of a weighted directed graph, with representing the weight of the arc from vertex i to vertex j.

Any n × n real symmetric matrix A determines a quadratic form q < sub > A </ sub > in n variables by the formula

Any symmetric matrix A can be transformed into a diagonal matrix

Any solution of the above set of equations following the constraints for is defined as the factors, and as the loading matrix.

Any real square matrix A may be decomposed as

If the operator is originally given by a square matrix M, then its Jordan normal form is also called the Jordan normal form of M. Any square matrix has a Jordan normal form if the field of coefficients is extended to one containing all the eigenvalues of the matrix.

Any block size could be specified up to the maximum track length.

Any interaction leads to a later elution time and thus mimics a smaller analyte size.

* Any array of any length can so be divided up into sections of size L ( x ).

Any increase or decrease in % C from 5 % increases the pore size, as pore size with respect to % C is a parabolic function with vertex as 5 % C.

Any farmer wishing to participate in the Small Farmers Scheme will receive an annual payment fixed by the Member State of between 500 € and 1 000 €, regardless of the farm ’ s size.

:# Any preferential treatment a person receives which is based on the size of the person's donation, is also offered to all other donors making a comparable contribution as part of a solicitation intended to attract a substantial number of contributions.

Any perfect hash functions suitable for use with a hash table require at least a number of bits that is proportional to the size of S.

Any treatment method must take into account the species of fish ( some will not tolerate certain medications ), how high the infection rate is, and the size and type of environment.

Any fees charged for financial transactions depend on a variety of factors, including the country's regulations and overall interest rates for lending and saving, as well as the financial institution's size and number of channels of access offered.

Any or all of these options can be utilized to trim the system out to its desired characteristics and many factors can contribute, such as the number and position of diving cylinders, the type of diving suit, the position and size of stage cylinders, the size and shape of the diver's body and the wearing of ankle weights, or additional dive equipment.

Any spaniel under 25 lb ( 11 kg ) was placed in the Cocker breeding pool, however the Welsh Cocker was reclassified as a Springer in 1903 due to its larger size and shorter ear.

Any object about the right size might serve as a puck.

Any expansion due to the temperature change of the coloured liquid and air gap inside the bulbs does not affect the operation of the thermometer, as these materials are sealed inside a glass bulb of fixed size.

Any size tumor may be removed with this approach.

Any similar triangles have the property that if we select the same angle in all them, the ratio of the two sides defining the angle is the same regardless of which similar triangle is selected, regardless of its actual size: the ratios depend upon the three angles, not the lengths of the sides.

Any non-singular matrix S of the same size is said to transform A into another symmetric matrix B = SAS < sup > T </ sup >, also of order n, where S < sup > T </ sup > is the transpose of S. If A is the coefficient matrix of some quadratic form of R < sup > n </ sup >, then B is the matrix for the same form after the change of coordinates defined by S.

Any business, regardless of size, can better manage supplier performance with the help of KPIs robust capabilities, which include:

Any increase in size of the bubble will decrease its potential energy, as the energy of the wall increases as the area of a sphere but the negative contribution of the interior increases more quickly, as the volume of a sphere.

Any row or column size may be replaced with an asterisk to indicate the remainder of the remaining screen space.

Any moon departure rocket must first be carried to the Moon's surface by a moon landing rocket, increasing the latter's required size.

Big Bore ( Any round that does not do target damage, full size targets, shot 50 / 100 / 150 / 200 Yards or Meters )