Rotation matrixIn linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system. To perform the rotation on a plane point with standard coordinates v = (x, y), it should be written as a column vector, and multiplied by the matrix R: If x and y are the endpoint coordinates of a vector, where x is cosine and y is sine, then the above equations become the trigonometric summation angle formulae.
ScienceScience is a rigorous, systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Modern science is typically divided into three major branches: natural sciences (e.g., biology, chemistry, and physics), which study the physical world; the social sciences (e.g., economics, psychology, and sociology), which study individuals and societies; and the formal sciences (e.g., logic, mathematics, and theoretical computer science), which study formal systems, governed by axioms and rules.
MultiplicationMultiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier; both numbers can be referred to as factors.
PhilosophyPhilosophy (love of wisdom in ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, values, mind, and language. It is a rational and critical inquiry that reflects on its own methods and assumptions. Historically, many of the individual sciences, like physics and psychology, formed part of philosophy. But they are considered separate academic disciplines in the modern sense of the term.
Multiplication signThe multiplication sign, also known as the times sign or the dimension sign, is the symbol , used in mathematics to denote the multiplication operation and its resulting product. While similar to a lowercase X (), the form is properly a four-fold rotationally symmetric saltire. The earliest known use of the symbol to represent multiplication appears in an anonymous appendix to the 1618 edition of John Napier's Mirifici Logarithmorum Canonis Descriptio.
Multiplication tableIn mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with base-ten numbers. Many educators believe it is necessary to memorize the table up to 9 × 9. The oldest known multiplication tables were used by the Babylonians about 4000 years ago.
Order of operationsIn mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression. For example, in mathematics and most computer languages, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. Thus, the expression 1 + 2 × 3 is interpreted to have the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9.
Statistical assumptionStatistics, like all mathematical disciplines, does not infer valid conclusions from nothing. Inferring interesting conclusions about real statistical populations almost always requires some background assumptions. Those assumptions must be made carefully, because incorrect assumptions can generate wildly inaccurate conclusions. Here are some examples of statistical assumptions: Independence of observations from each other (this assumption is an especially common error). Independence of observational error from potential confounding effects.
TransposeIn linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by AT (among other notations). The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. In the case of a logical matrix representing a binary relation R, the transpose corresponds to the converse relation RT.
Reading comprehensionReading comprehension is the ability to process written text, understand its meaning, and to integrate with what the reader already knows. Reading comprehension relies on two abilities that are connected to each other: word reading and language comprehension. Comprehension specifically is a "creative, multifaceted process" dependent upon four language skills: phonology, syntax, semantics, and pragmatics.
Linear actuatorA linear actuator is an actuator that creates motion in a straight line, in contrast to the circular motion of a conventional electric motor. Linear actuators are used in machine tools and industrial machinery, in computer peripherals such as disk drives and printers, in valves and dampers, and in many other places where linear motion is required. Hydraulic or pneumatic cylinders inherently produce linear motion. Many other mechanisms are used to generate linear motion from a rotating motor.
Wernicke's areaWernicke's area (ˈvɛərnᵻkə; ˈvɛɐ̯nɪkə), also called Wernicke's speech area, is one of the two parts of the cerebral cortex that are linked to speech, the other being Broca's area. It is involved in the comprehension of written and spoken language, in contrast to Broca's area, which is primarily involved in the production of language. It is traditionally thought to reside in Brodmann area 22, which is located in the superior temporal gyrus in the dominant cerebral hemisphere, which is the left hemisphere in about 95% of right-handed individuals and 70% of left-handed individuals.
