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Matrix representation of conic sections

In mathematics, the matrix representation of conic sections permits the tools of linear algebra to be used in the study of conic sections. It provides easy ways to calculate a conic section's axis, vertices and the pole and polar relationship between points and lines of the plane determined by the conic; the technique does not require putting the equation of a conic section into a standard form, thus making it easier to investigate those conic sections whose axes are not parallel to the coordinate system. Conic sections are the sets of points whose coordinates satisfy a second-degree polynomial equation, Q = A x 2 + B x y + C y 2 + D x + E y + F = 0. By an abuse of notation, this conic section will be called Q when no confusion can arise; this equation can be written in matrix notation, in terms of a symmetric matrix to simplify some subsequent formulae, as + + F = 0. The sum of the first three terms of this equation, namely A x 2 + B x y + C y 2 =, is the quadratic form associated with the equation, the matrix A 33 = is called the matrix of the quadratic form.

The trace and determinant of A 33 are both invariant with respect to rotation of axes and translation of the plane. The quadratic equation can be written as x T A Q x = 0, where x is the homogeneous coordinate vector in three variables restricted so that the last variable is 1, i.e. and where A Q is the matrix A Q =. The matrix A Q is called the matrix of the quadratic equation. Like that of A 33, its determinant is invariant with respect to both translation; the 2 × 2 upper left submatrix of AQ, obtained by removing the third row and third column from AQ is the matrix of the quadratic form. The above notation A33 is used in this article to emphasize this relationship. Proper and degenerate conic sections can be distinguished based on the determinant of AQ. If det A Q = 0, the conic is degenerate. If det A Q ≠ 0 so that Q is not degenerate, we can see what type of conic section it is by computing the minor, det A 33: Q is a hyperbola if and only if det A 33 < 0, Q is a parabola if and only if det A 33 = 0, Q is an ellipse if and only if det A 33 > 0.

In the case of an ellipse, we can distinguish the special case of a circle by comparing the last two diagonal elements

Water ball

A water ball or water walking ball is a large inflatable sphere that allows a person inside it to walk across the surface of a body of water. The giant ball is two metres in diameter and has a zippered entrance to allow for easy entry and exit; the water ball is similar to the zorb but it has only one layer and is designed for water travel rather than down-hill rolling. In the United Kingdom, the balls have been used at swimming pools and lakes in an effort to keep children fit. One of the first water balls appeared in the film Diamonds Are Forever and in the Beach Boys music video, Getcha Back. Charles Blane Jones designed the first water ball for public distribution in 1998. Water balls have been used safely in over 50 countries around the world since 1998. However, 99% of the amusement business uses the water balls in safe confined inflatable swimming pools with water levels that do not exceed 2 ft. and are under complete supervision at all times by trained and competent staff. Charles Jones from Oklahoma developed a water ball commercially in 1998.

He was invited by a British reporter to visit London to demonstrate the ball on a lake. As soon as he attempted to walk across the water, he fell; the ball deflated and filled with icy water. He was saved from sinking below the surface when an assistant dragged the ball back to dry land using a safety line, witnessed by a crowd of tourists; the U. S. Consumer Product Safety Commission has warned of the dangers of the balls being used in a safe manner; the Commission is aware of two unconfirmed incidents involving water balls. In one, a child was found unresponsive after being inside the ball for a brief period of time. After being examined, the child was found to be suffering from an unrelated ongoing medical problem. In the second incident, a person inside the ball suffered a fracture when it fell out of a shallow, above-ground pool onto hard ground. Many water balls are constructed from polyvinyl chloride 0.8–1.0 mm thick. Thermoplastic polyurethanes are the best choice on snow; some water balls are made from a PVC–TPU mix.

More expensive balls use 100% TPU. Balls are made in China, come in various sizes. A typical water ball stores flat and weighs 15 kilograms, can be inflated in under a minute with a good air pump; some models have hand grips on the inside or outside, the surface can be printed on. Zorbing Hamster ball List of inflatable manufactured goods

George Blake (novelist)

George Blake was a Scottish journalist, literary editor and novelist. His The Shipbuilders is considered a significant and influential effort to write about the Scottish industrial working class. "At a time when the idea of myth was current in the Scottish literary world and other writers were forging theirs out of the facts and spirit of rural life, Blake took the iron and grease and the pride of the skilled worker to create one for industrial Scotland." As a literary critic, he wrote a noted work against the Kailyard school of Scottish fiction. He was well known as a BBC radio broadcaster by the 1930s, he was born in Greenock, the son of Matthew Blake, machinery manufacturer, his wife Ursula Scott McCulloch. He was educated at Glasgow University, he trained as a solicitor. During World War I he was wounded during the Gallipoli Campaign. After the war Blake worked at the Glasgow Evening News, where Neil Munro was editor from 1918. At this period he had contact with Red Clydeside through his dramatic works, sitting on the council of the Scottish National Players.

As a playwright, he came under the influence of Andrew P. Wilson. Blake moved to London where he stayed from 1924 to 1932. There he was an editor of John O'London's Weekly, replacing Sidney Dark as subeditor and writing a number of columns, to 1928; the Porpoise Press, in existence from 1922 to 1939, was founded in Edinburgh by Roderick Watson Kerr and George Malcolm Thomson. Blake had contact with Thomson from 1923. Thomson's 1927 book Caledonia broached the "condition of Scotland" question that preoccupied Blake and other Scottish intellectuals into the 1930s. Late in 1929, Blake was introduced by Frank Vigor Morley, he became in 1930 a director of Faber & Faber, playing a role in the Porpoise Press: Faber & Faber took it over, through interest in Scottish national literature. Morning Tide, a novel by Neil Gunn, was an immediate commercial success for the Press. At this point Thomson and Blake were aligned in nationalist politics. Thomson's 1931 pamphlet The Kingdom of Scotland Restored, advocating a form of Scottish home rule, had Blake's approval, the Introduction was signed by Blake, Andrew Dewar Gibb, Moray McLaren and William Power.

By that year, Blake had joined the National Party of Scotland. Gunn became involved in the efforts, which succeeded, to merge the NPS, of the left, with the conservative Scottish Party. Returning to Scotland in 1932, Blake worked for the Porpoise Press, which in 1934 published William Power's My Scotland. Both Gibb and Power became leaders of the merged Scottish National Party. Blake and Thomson fell out, with Thomson resigning from the Press in 1933, it published his Scotland That Distressed Area in 1935. Blake's The Shipbuilders was published the same year, by Faber, they differed in method: Thomson offered partisan polemics, Blake a journalist's realism expressed as a novel. Blake lived at The Glenan and elsewhere, he was literary journalist. He had a regular position on This Week in BBC Scottish Region Radio; this was despite some reservations on the part of Andrew Stewart, Scottish Programme Director, who thought Blake's nationalist views were too overt, would have preferred Eric Linklater. Blake died in Glasgow's Southern General Hospital on 29 August 1961, survived by his wife Eliza Malcolm Lawson, whom he had married in 1923.

Blake's novels have been described as "resolutely realistic, serious and nationalistic". Their social realism included addressing industrialisation and urban poverty, topics neglected in Scottish literature until the 1920s and 1930s, he wrote a number of "Glasgow novels", as well as other fiction. Hugh Macdiarmid discussed in 1926 a "new Glasgow school" of novelists, listing figures of whom only Catherine Carswell attained the same sort of stature as Blake. Mince Collop Close The Wild Men ) Young Malcolm ) Paper Money, US title Gettin' in Society The Path of Glory, about the Gallipoli campaign, in the "soldier's tale" genre. Returned Empty The Shipbuilders, subsequently a film The Shipbuilders from 1943; the film has been described as a more authentic representation of working-class Glasgow. James Kelman took the novel's third-person narrative as exemplary of narrative laden with a value system. David and Joanna Down to the Sea, autobiographical "Garvel" novel series. After Late Harvest came The Valiant Heart, The Constant Star, The Westering Sun, The Paying Guest, The Voyage Home.

The Piper's Tune, Clydeside The Peacock Palace Floodtide was a feature film with a screenplay involving Blake. The Mother, produced 13 April 1921 with Elliot Cranston Mason as Morag Gillespie. Fledglings, performed 1922 by the Scottish National Players. Clyde Built The Weaker Vessel In life, Blake wrote factually about Clydeside and shipping lines. "Blake's thesis is that the history of the Clyde is a glorious tale of great ships, born out of traditions of craftsmanship and mechanical genius unrivalled anywhere in the world." Vagabond Papers The Press and the Public The Heart of Scotland and editions

Gary Walsh (Gaelic footballer)

Gary Walsh is an Irish former Gaelic footballer who played as goalkeeper for Aodh Ruadh and the Donegal county team. He is from Ballyshannon; as of 2009, he worked as an accountant with Derry City Council. Walsh was a member of Donegal's 1992 All-Ireland Senior Football Championship winning team and played for the county from 1984 until 1996, he played as a goalkeeper and only conceded three goals in six matches in the 1992 championship season. He won an All Star Award. Walsh won two Down Senior Football Championships with Burren. After retiring, Walsh assisted Brian McEniff as a goalkeeping coach when McEniff returned as Donegal manager in the early 2000s. DonegalAll-Ireland Senior Football Championship: 1992 Ulster Senior Football Championship: 1990, 1992BurrenDown Senior Football Championship: 1996, 1997IndividualAll Star: 1992 Gary Walsh at Profile Hogan Stand

Polygonum erectum

Polygonum erectum called erect knotweed, is a North American species of herbaceous plant in the buckwheat family. It is found in the northeastern and north-central parts of the United States, but with scattered populations in other parts of the US and in Canada, its natural habitat is in bottomland forests and riparian areas. It is tolerant of ecological degradation, can be found in disturbed open areas such as pastures and lawns, it was once cultivated for food by Native Americans as part of the group of crops known as the Eastern Agricultural Complex. Polygonum erectum is an erect annual growing 10–75 cm tall with many to few, non-wiry branches; the leaves have jagged cut edges. The pedicels are shorter or equal the length of the calyx and longer than the ocreae; the closed flowers have a calyx, 3 mm long, green in color and 5-lobed. Flowers in clusters of 1 to 5 in cymes that are produced in the axils of most leaves; the calyx segments are unequal with the outer lobes longer and not keeled and the inner ones narrowly keeled.

The tepals are greenish, with yellowish tinting or sometimes with whitish tints. The seeds are produced in fruits called achenes; the other achene type is dull brown and egg-shaped, 3–3.5 mm long. Late season fruiting is uncommon. Polygonum erectum is considered to be globally secure. However, it is uncommon throughout much of its range, population have declined in some regions, it is listed as endangered in New Hampshire and New York

Ecology Party of Florida

The Ecology Party of Florida is a minor political party in the United States state of Florida. Founded as a front group to support Ralph Nader's 2008 presidential candidacy, it has remained minimally active in the years since that election; the party, which describes itself as "peacefully revolutionary", was founded by supporters of Ralph Nader in 2008. The party was formed to give Nader easy access to the Florida ballot line in that year's election; the party nominated Nader for president of the United States in 2008. Nader accepted the nomination and appeared on the ballot in Florida as a candidate of the Ecology Party of Florida, while running in most other states as independent or unaffiliated. In 2009 the party registered as a co-intervener in an attempt to stop administrative licensing of two proposed nuclear reactors in Levy County, Florida. Contributions from an anonymous donor allowed the party to retain legal representation in support of its efforts; the party did not nominate a candidate in the 2012 presidential election.

In 2015 the party joined with a number of other groups, including Greenpeace, the Tea Party Network, Sierra Club, Conservatives for Responsible Stewardship, in pushing a ballot initiative in Florida that, if passed, would permit businesses to produce up to two megawatts of solar power per day and sell it directly to businesses and residences on adjacent property. Official website