Let V=M2(R) denote the vector space 2x2 matrices with real entries over the field. Let T:V→V be defined by T(P) = Pt for any P∈V, where Pt is the transpose of P. If E is the matrix representation of T with respect to the standard basis of V the det(E) is equal to
If the Newton-Raphson method is applied to find a
real root of f(x) = 2x2 + x - 2 = 0 with initial approximation x0 = 1. Then the second approximation x2 is
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I'd been working with plastic bags, which I cut up and sew back together as my primary material for my artwork for the last 20 years. I turn them into two and three-dimensional pieces and sculptures and installations. After about the first eight years, some of my work started to fissure and break down into smaller little bits of plastic. It's a bad thing that plastic breaks down into smaller little bits, because it's always still plastic. And a lot of it is in the marine environment. I learned about the Pacific garbage patch. I wanted to go out there, pick up the plastic, and cold mold it into bricks to be used as building materials in underdeveloped communities. But soon I realized that I needed to look at the bigger picture first: we need to attack the source of this waste that is entering the marine environment every day on a global scale. Rather marine environment every day on a global scale. Rather than the marine plastic pile what I should focus on, is the pile of plastic in the supermarket. I'd go to the supermarket and all of my food is packaged in plastic. I'm concerned about the plastic and the toxins that leach from plastic into us and into our bodies.
How did the writer come to be concerned about plastic waste?
Read the following passage and answer the subsequent questions :
I'd been working with plastic bags, which I cut up and sew back together as my primary material for my artwork for the last 20 years. I turn them into two and three-dimensional pieces and sculptures and installations. After about the first eight years, some of my work started to fissure and break down into smaller little bits of plastic. It's a bad thing that plastic breaks down into smaller little bits, because it's always still plastic. And a lot of it is in the marine environment. I learned about the Pacific garbage patch. I wanted to go out there, pick up the plastic, and cold mold it into bricks to be used as building materials in underdeveloped communities. But soon I realized that I needed to look at the bigger picture first: we need to attack the source of this waste that is entering the marine environment every day on a global scale. Rather marine environment every day on a global scale. Rather than the marine plastic pile what I should focus on, is the pile of plastic in the supermarket. I'd go to the supermarket and all of my food is packaged in plastic. I'm concerned about the plastic and the toxins that leach from plastic into us and into our bodies.
Read the following passage and answer the subsequent questions :
I'd been working with plastic bags, which I cut up and sew back together as my primary material for my artwork for the last 20 years. I turn them into two and three-dimensional pieces and sculptures and installations. After about the first eight years, some of my work started to fissure and break down into smaller little bits of plastic. It's a bad thing that plastic breaks down into smaller little bits, because it's always still plastic. And a lot of it is in the marine environment. I learned about the Pacific garbage patch. I wanted to go out there, pick up the plastic, and cold mold it into bricks to be used as building materials in underdeveloped communities. But soon I realized that I needed to look at the bigger picture first: we need to attack the source of this waste that is entering the marine environment every day on a global scale. Rather marine environment every day on a global scale. Rather than the marine plastic pile what I should focus on, is the pile of plastic in the supermarket. I'd go to the supermarket and all of my food is packaged in plastic. I'm concerned about the plastic and the toxins that leach from plastic into us and into our bodies.
Read the following passage and answer the subsequent questions :
I'd been working with plastic bags, which I cut up and sew back together as my primary material for my artwork for the last 20 years. I turn them into two and three-dimensional pieces and sculptures and installations. After about the first eight years, some of my work started to fissure and break down into smaller little bits of plastic. It's a bad thing that plastic breaks down into smaller little bits, because it's always still plastic. And a lot of it is in the marine environment. I learned about the Pacific garbage patch. I wanted to go out there, pick up the plastic, and cold mold it into bricks to be used as building materials in underdeveloped communities. But soon I realized that I needed to look at the bigger picture first: we need to attack the source of this waste that is entering the marine environment every day on a global scale. Rather marine environment every day on a global scale. Rather than the marine plastic pile what I should focus on, is the pile of plastic in the supermarket. I'd go to the supermarket and all of my food is packaged in plastic. I'm concerned about the plastic and the toxins that leach from plastic into us and into our bodies.
Read the following passage and answer the subsequent questions :
Recycling – everybody kind of ends their books about being sustainable and greening with the idea of recycling. You put something in a bin and you don't have to think about it again. What is the reality of that? In the United States, less than seven percent of the plastics are recycled, or incinerated, or shipped to China. It is down-cycled and turned into lesser things -- a plastic bottle can never be a plastic bottle again. We, a group of people concerned about plastic pollution, have added a fourth R onto the front of the "Reduce, Reuse, Recycle," and that is refuse. Whenever possible, refuse single-use and disposable plastics. Alternatives exist; I myself am now collecting these cool Pyrex containers and using those instead of plastic containers to store food in. And I know that I am doing a service to myself and my family. It is a problem that we've created as consumers and we have to solve it –We can solve this by raising awareness of the issue and teaching people to choose alternatives.
Why does the author think recycling is not the right solution?
Read the following passage and answer the subsequent questions :
Recycling – everybody kind of ends their books about being sustainable and greening with the idea of recycling. You put something in a bin and you don't have to think about it again. What is the reality of that? In the United States, less than seven percent of the plastics are recycled, or incinerated, or shipped to China. It is down-cycled and turned into lesser things -- a plastic bottle can never be a plastic bottle again. We, a group of people concerned about plastic pollution, have added a fourth R onto the front of the "Reduce, Reuse, Recycle," and that is refuse. Whenever possible, refuse single-use and disposable plastics. Alternatives exist; I myself am now collecting these cool Pyrex containers and using those instead of plastic containers to store food in. And I know that I am doing a service to myself and my family. It is a problem that we've created as consumers and we have to solve it –We can solve this by raising awareness of the issue and teaching people to choose alternatives.
Read the following passage and answer the subsequent questions :
Recycling – everybody kind of ends their books about being sustainable and greening with the idea of recycling. You put something in a bin and you don't have to think about it again. What is the reality of that? In the United States, less than seven percent of the plastics are recycled, or incinerated, or shipped to China. It is down-cycled and turned into lesser things -- a plastic bottle can never be a plastic bottle again. We, a group of people concerned about plastic pollution, have added a fourth R onto the front of the "Reduce, Reuse, Recycle," and that is refuse. Whenever possible, refuse single-use and disposable plastics. Alternatives exist; I myself am now collecting these cool Pyrex containers and using those instead of plastic containers to store food in. And I know that I am doing a service to myself and my family. It is a problem that we've created as consumers and we have to solve it –We can solve this by raising awareness of the issue and teaching people to choose alternatives.
Read the following passage and answer the subsequent questions :
Milk contains a type of sugar called lactose. When we are babies, our bodies make a special enzyme called lactase that allows us to digest the lactose in our mother‟s milk. But after we are weaned in early childhood, for many people this stops. Without lactase, we cannot properly digest the lactose in milk. But then evolution kicked in: some people began to keep their lactase enzymes active into adulthood. This “lactase persistence” allowed them to drink milk without side effects. It is the result of mutations in a section of DNA that controls the activity of the lactase gene. But in many populations, such as those in Africa, in Asia and South America, the trait is uncommon. Even people who are lactase-non-persistent exploit the option of processing milk into butter, yoghurt, cream or cheese – all of which have reduced amount of lactose. There is clearly a pattern behind which populations evolved high levels of lactase persistence and which didn‟t, says a genetics professor Dallas Swallow of University College London. Those with the trait are pastoralists: people who raise livestock. Hunter-gatherers, who do not keep animals, did not acquire the mutations. Neither did “forest gardeners” who cultivated plants. But milk consumption is going down, says a study. Statistics tell a different story. While milk consumption has fallen in the US, in Asia demand is growing, where most people are non-lactase-persistent. Whatever advantages the people there see in milk, they outweigh the potential digestive issues or the need to process the milk.
Why is it that some grownups can drink and digest milk while others cannot digest it?
Read the following passage and answer the subsequent questions :
Milk contains a type of sugar called lactose. When we are babies, our bodies make a special enzyme called lactase that allows us to digest the lactose in our mother‟s milk. But after we are weaned in early childhood, for many people this stops. Without lactase, we cannot properly digest the lactose in milk. But then evolution kicked in: some people began to keep their lactase enzymes active into adulthood. This “lactase persistence” allowed them to drink milk without side effects. It is the result of mutations in a section of DNA that controls the activity of the lactase gene. But in many populations, such as those in Africa, in Asia and South America, the trait is uncommon. Even people who are lactase-non-persistent exploit the option of processing milk into butter, yoghurt, cream or cheese – all of which have reduced amount of lactose. There is clearly a pattern behind which populations evolved high levels of lactase persistence and which didn‟t, says a genetics professor Dallas Swallow of University College London. Those with the trait are pastoralists: people who raise livestock. Hunter-gatherers, who do not keep animals, did not acquire the mutations. Neither did “forest gardeners” who cultivated plants. But milk consumption is going down, says a study. Statistics tell a different story. While milk consumption has fallen in the US, in Asia demand is growing, where most people are non-lactase-persistent. Whatever advantages the people there see in milk, they outweigh the potential digestive issues or the need to process the milk.
How did some populations come to retain lactase-persistence while very many others did not as they grew up?
Read the following passage and answer the subsequent questions :
Milk contains a type of sugar called lactose. When we are babies, our bodies make a special enzyme called lactase that allows us to digest the lactose in our mother‟s milk. But after we are weaned in early childhood, for many people this stops. Without lactase, we cannot properly digest the lactose in milk. But then evolution kicked in: some people began to keep their lactase enzymes active into adulthood. This “lactase persistence” allowed them to drink milk without side effects. It is the result of mutations in a section of DNA that controls the activity of the lactase gene. But in many populations, such as those in Africa, in Asia and South America, the trait is uncommon. Even people who are lactase-non-persistent exploit the option of processing milk into butter, yoghurt, cream or cheese – all of which have reduced amount of lactose. There is clearly a pattern behind which populations evolved high levels of lactase persistence and which didn‟t, says a genetics professor Dallas Swallow of University College London. Those with the trait are pastoralists: people who raise livestock. Hunter-gatherers, who do not keep animals, did not acquire the mutations. Neither did “forest gardeners” who cultivated plants. But milk consumption is going down, says a study. Statistics tell a different story. While milk consumption has fallen in the US, in Asia demand is growing, where most people are non-lactase-persistent. Whatever advantages the people there see in milk, they outweigh the potential digestive issues or the need to process the milk.
Average of ten numbers in a list is 25.If one of the numbers in the list is exchanged with another number the average of the new list increases by 5. What is the new number included in the list , if the original number was 15?