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[2]: 396 The bacterial flagellum is the best known example. [27] [28] About half of all known bacteria have at least one flagellum; thus, given the ubiquity of bacteria, rotation may in fact be the most common form of locomotion used by living systems—though its use is restricted to the microscopic environment. [29]
A life history strategy is the "age- and stage-specific patterns" [2] and timing of events that make up an organism's life, such as birth, weaning, maturation, death, etc. [3] These events, notably juvenile development, age of sexual maturity, first reproduction, number of offspring and level of parental investment, senescence and death, depend ...
In biology, evolution is any change across successive generations in the heritable characteristics of biological populations. Evolutionary processes give rise to diversity at every level of biological organization , from kingdoms to species , and individual organisms and molecules , such as DNA and proteins .
The rotation, restricted to this plane, is an ordinary 2D rotation. The proof proceeds similarly to the above discussion. First, suppose that all eigenvalues of the 3D rotation matrix A are real. This means that there is an orthogonal basis, made by the corresponding eigenvectors (which are necessarily orthogonal), over which the effect of the ...
For example, to study the equations of ellipses and hyperbolas, the foci are usually located on one of the axes and are situated symmetrically with respect to the origin. If the curve (hyperbola, parabola , ellipse, etc.) is not situated conveniently with respect to the axes, the coordinate system should be changed to place the curve at a ...
On the Sun, the study of oscillations revealed that rotation is roughly constant within the whole radiative interior and variable with radius and latitude within the convective envelope. The Sun has an equatorial rotation speed of ~2 km/s; its differential rotation implies that the angular velocity decreases with increased latitude.
A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L 1. Then reflect P′ to its image P′′ on the other side of line L 2. If lines L 1 and L 2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...
A rotation of the vector through an angle θ in counterclockwise direction is given by the rotation matrix: = ( ), which can be viewed either as an active transformation or a passive transformation (where the above matrix will be inverted), as described below.