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If it's closed then matter can't be added or taken away from the system, such as a closed box, but heat can still transfer into and out of it. If the system is isolated, then it's like a highly insulated box where matter and heat both can't be transferred into or out of the system.
In reference to the plant question, any biological organism is considered an open system. This is because all organisms that we know of today interact with their environment in various ways. Plants take in matter through the air and ground, which is used to grow, and also utilize solar energy from their surroundings. Animals are similar in that they take in matter through their mouth/nose and can freely exchange energy with their surroundings (Think of the sunlight warming you up, or your hand getting cold when you touch an ice cube). Cells act this way as well since they take in matter (various chemicals, hormones, etc) and also respond to energy changes (nerve cells).
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