Linear groupIn mathematics, a matrix group is a group G consisting of invertible matrices over a specified field K, with the operation of matrix multiplication. A linear group is a group that is isomorphic to a matrix group (that is, admitting a faithful, finite-dimensional representation over K). Any finite group is linear, because it can be realized by permutation matrices using Cayley's theorem. Among infinite groups, linear groups form an interesting and tractable class.
Ice sheetIn glaciology, an ice sheet, also known as a continental glacier, is a mass of glacial ice that covers surrounding terrain and is greater than . The only current ice sheets are in Antarctica and Greenland; during the Last Glacial Period at Last Glacial Maximum, the Laurentide Ice Sheet covered much of North America, the Weichselian ice sheet covered Northern Europe and the Patagonian Ice Sheet covered southern South America. Ice sheets are bigger than ice shelves or alpine glaciers.
IceIce is water frozen into a solid state, typically forming at or below temperatures of 32 °F, 0 °C, or 273.15 K. Depending on the presence of impurities such as particles of soil or bubbles of air, it can appear transparent or a more or less opaque bluish-white color. In the Solar System, ice is abundant and occurs naturally from as close to the Sun as Mercury to as far away as the Oort cloud objects. Beyond the Solar System, it occurs as interstellar ice.
Sea iceSea ice arises as seawater freezes. Because ice is less dense than water, it floats on the ocean's surface (as does fresh water ice, which has an even lower density). Sea ice covers about 7% of the Earth's surface and about 12% of the world's oceans. Much of the world's sea ice is enclosed within the polar ice packs in the Earth's polar regions: the Arctic ice pack of the Arctic Ocean and the Antarctic ice pack of the Southern Ocean.
ExerciseExercise is a body activity that enhances or maintains physical fitness and overall health and wellness. It is performed for various reasons, including weight loss or maintenance, to aid growth and improve strength, develop muscles and the cardiovascular system, hone athletic skills, improve health, or simply for enjoyment. Many individuals choose to exercise outdoors where they can congregate in groups, socialize, and improve well-being as well as mental health.
Polar ice capA polar ice cap or polar cap is a high-latitude region of a planet, dwarf planet, or natural satellite that is covered in ice. There are no requirements with respect to size or composition for a body of ice to be termed a polar ice cap, nor any geological requirement for it to be over land, but only that it must be a body of solid phase matter in the polar region. This causes the term "polar ice cap" to be something of a misnomer, as the term ice cap itself is applied more narrowly to bodies that are over land, and cover less than 50,000 km2: larger bodies are referred to as ice sheets.
Geometric group theoryGeometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces). Another important idea in geometric group theory is to consider finitely generated groups themselves as geometric objects.
Exercise physiologyExercise physiology is the physiology of physical exercise. It is one of the allied health professions, and involves the study of the acute responses and chronic adaptations to exercise. Exercise physiologists are the highest qualified exercise professionals and utilise education, lifestyle intervention and specific forms of exercise to rehabilitate and manage acute and chronic injuries and conditions.
Felix KleinChristian Felix Klein (klaɪn; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory. His 1872 Erlangen program, classifying geometries by their basic symmetry groups, was an influential synthesis of much of the mathematics of the time. Felix Klein was born on 25 April 1849 in Düsseldorf, to Prussian parents.
Aerobic exerciseAerobic exercise (also known as endurance activities, cardio or cardio-respiratory exercise) is physical exercise of low to high intensity that depends primarily on the aerobic energy-generating process. "Aerobic" is defined as "relating to, involving, or requiring oxygen", and refers to the use of oxygen to meet energy demands during exercise via aerobic metabolism adequately. Aerobic exercise is performed by repeating sequences of light-to-moderate intensity activities for extended periods of time.
Neurobiological effects of physical exerciseThe neurobiological effects of physical exercise are numerous and involve a wide range of interrelated effects on brain structure, brain function, and cognition. A large body of research in humans has demonstrated that consistent aerobic exercise (e.g., 30 minutes every day) induces persistent improvements in certain cognitive functions, healthy alterations in gene expression in the brain, and beneficial forms of neuroplasticity and behavioral plasticity; some of these long-term effects include: increased neuron growth, increased neurological activity (e.
Atmosphere of EarthThe atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth creates pressure, absorbs most meteoroids and ultraviolet solar radiation, warms the surface through heat retention (greenhouse effect), allowing life and liquid water to exist on the Earth's surface, and reduces temperature extremes between day and night (the diurnal temperature variation). As of 2023, by mole fraction (i.
