Prova EFOMM 2021 comentada: questões e gabarito

EFOMM2021Dia 2Questao 1MatemáticaDeterminantesMedia

Considere uma equação definida por

det lo g x 4^{x} 0 lo g x^{4} 1 6^{x} 0 lo g x^{16} 6 4^{x} 2 = 0, \forall x > 0

Sabendo-se que a solução da equação acima é o número de elementos de um conjunto A, é correto afirmar que o número de subconjuntos que se pode formar com esse conjunto é igual a

A)0
B)1
C)2
D)3
E)4

EFOMM2021Dia 1Questao 1InglêsInterpretação de textoFacil

Development of world's first autonomous, zero-emission feeder postponed amid COVID-19 crisis Due to the COVID-19 pandemic and the changed global outlook, the development of the world's first autonomous and electric container vessel Yara Birkeland is put on hold, Norwegian company Yara announced. Yara has decided to pause further development of the vessel and will assess next steps together with its partners, the company stated. The hull of the Yara Birkeland vessel was launched to sea in Romania in February 2020. The ship is expected to arrive at the Norwegian shipyard in May where it will be fitted with various control and navigation systems and undergo testing before delivery to Yara. Yara and technology company Kongsberg teamed up in 2017 with the ambition to build the world's first autonomous and zero-emission container vessel. Replacing 40,000 truck journeys a year, Yara Birkeland seeks to reduce NOx and CO2 emissions and improve road safety in a densely populated urban area in Norway. (Adapted from: https://safety4sea.com) According to the article:

A)Covid-19 pandemic urged the development of the world's first autonomous, zero-emission feeder.
B)Norwegian Company Yara issued a statement about the launching of a new watercraft fully manned.
C)Unmanned craft can whittle down the discharge of foul air and greenhouse gases.
D)Yara and Kongsberg technology company split up due to the virus outbreak.
E)Autonomous and zero-emission feeders are salvage vessels that can stow the level of pollutants.

EFOMM2021Dia 1Questao 2InglêsVocabulário e expressões idiomáticasFacil

Development of world's first autonomous, zero-emission feeder postponed amid COVID-19 crisis Due to the COVID-19 pandemic and the changed global outlook, the development of the world's first autonomous and electric container vessel Yara Birkeland is put on hold, Norwegian company Yara announced. Yara has decided to pause further development of the vessel and will assess next steps together with its partners, the company stated. The hull of the Yara Birkeland vessel was launched to sea in Romania in February 2020. The ship is expected to arrive at the Norwegian shipyard in May where it will be fitted with various control and navigation systems and undergo testing before delivery to Yara. Yara and technology company Kongsberg teamed up in 2017 with the ambition to build the world's first autonomous and zero-emission container vessel. Replacing 40,000 truck journeys a year, Yara Birkeland seeks to reduce NOx and CO2 emissions and improve road safety in a densely populated urban area in Norway. (Adapted from: https://safety4sea.com) In "[...] Yara Birkeland is put on hold [...].", the idiom in bold means:

A)Put away
B)Put about
C)Put off
D)Put across
E)Put up

EFOMM2021Dia 2Questao 2MatemáticaMatrizesMedia

Dadas as matrizes reais 2x2 do tipo

A (x) = (cos x sen x sen x cos x)

, pode-se afirmar que I.

A (x)

é inversível. II.

\exists x \in [0, 2 π]

tal que

A (x) A (x) = A (x)

. III.

A (x)

nunca será antissimétrica. Assinale a opção correta.

A)Apenas as afirmativas I e II são verdadeiras.
B)Apenas as afirmativas I e III são verdadeiras.
C)Apenas as afirmativas II e III são verdadeiras.
D)Apenas a afirmativa I é verdadeira.
E)Apenas a afirmativa II é verdadeira.

EFOMM2021Dia 1Questao 3InglêsInterpretação de textoMedia

Development of world's first autonomous, zero-emission feeder postponed amid COVID-19 crisis Due to the COVID-19 pandemic and the changed global outlook, the development of the world's first autonomous and electric container vessel Yara Birkeland is put on hold, Norwegian company Yara announced. Yara has decided to pause further development of the vessel and will assess next steps together with its partners, the company stated. The hull of the Yara Birkeland vessel was launched to sea in Romania in February 2020. The ship is expected to arrive at the Norwegian shipyard in May where it will be fitted with various control and navigation systems and undergo testing before delivery to Yara. Yara and technology company Kongsberg teamed up in 2017 with the ambition to build the world's first autonomous and zero-emission container vessel. Replacing 40,000 truck journeys a year, Yara Birkeland seeks to reduce NOx and CO2 emissions and improve road safety in a densely populated urban area in Norway. (Adapted from: https://safety4sea.com) Which statements are TRUE about the article? I - The pandemic forestalled additional improvement of the feeder vessel. II - The ship will enable a depletion of road freight and road hazards. III - The vessel will be scrapped straight away. IV - The Norwegian shipyard went bankrupt due to the changed global outlook. V - The ship will be fitted with outdated controls and navigation systems.

A)I and V
B)IV and V
C)II and V
D)III and IV
E)I and II

EFOMM2021Dia 2Questao 3MatemáticaTrigonometria e vetoresMedia

O valor de

\frac{sec ^{2} ( 5 ) + cossec ^{2} ( 5 )}{cossec ^{2} ( 10 )}

é igual a:

A) $\frac{1}{2}$
B)1
C)2
D) $\frac{5}{2}$
E)4

EFOMM2021Dia 2Questao 4MatemáticaLogaritmos e funçõesDificil

Sejam f e g funções reais definidas por

f (x) = {2^{x}, x, x \geq 1 x < 1

e

g (x) = {1 - x^{2}, x^{2} - 1, x \geq 0 x < 0

Sendo assim, pode-se dizer que

f \circ g (x)

é definida por

A) $f \circ g (x) = ⎩ ⎨ ⎧ 1 - x^{2}, 2^{1 - x^{2}}, x^{2} - 1, 2^{x^{2} - 1}, x > 0 x = 0 - 2 < x < 0 x \leq - 2$
B) $f \circ g (x) = ⎩ ⎨ ⎧ x^{2} - 1, 2^{1 - x^{2}}, 1 - x^{2}, 2^{x^{2} - 1}, x = 0 x > 0 - 2 \leq x < 0 x < - 2$
C) $f \circ g (x) = ⎩ ⎨ ⎧ 1 - x^{2}, 2^{1 - x^{2}}, x^{2} - 1, 2^{x^{2} - 1}, x > 0 x = 0 - 2 < x \leq 0 x \leq - 2$
D) $f \circ g (x) = ⎩ ⎨ ⎧ 1 - x^{2}, 2^{1 - x^{2}}, x^{2} - 1, 2^{x^{2} - 1}, 0 < x < 1 x = 0 - 2 \leq x \leq 0 x < - 2$
E) $f \circ g (x) = ⎩ ⎨ ⎧ 1 - x^{2}, 2^{1 - x^{2}}, x^{2} - 1, 2^{x^{2} - 1}, x \geq 1 0 \leq x < 1 - 2 \leq x < 0 x < - 2$

EFOMM2021Dia 1Questao 4InglêsInterpretação de textoMedia

Passenger ship hits rock A passenger ship was inbound in daylight and fair visibility. The Master gave the Pilot a briefing regarding the ship's manoeuvring characteristics; the ship was highly manoeuvrable and would 'turn on a dime,' he said. The Master told the Pilot that a three-degree helm order would create a rate of turn of 10-15 degrees per minute. The bridge team would consist of the Pilot at the con while the Master would have overall navigational command. The staff captain would be in charge of communications while the first officer would be in charge of electronic navigation and collision avoidance. Finally, the second officer would be in charge of plotting the ship's position on the navigational chart. The Pilot and the Master discussed and agreed the intended passage plan, noting a strong flood tide that would be running astern. However, the subsequent investigation found that, due to miscommunication during the exchange, the passage inwards began with the Master and Pilot having different understandings of how the first turn would be conducted. The ship was lined up with the leading navigation lights and entered the channel without incident. As the Pilot took the con, the Master briefed the staff captain on the Master/ Pilot exchange and explained his understanding of how they were going to negotiate the turn to port. The rest of the bridge team were not included in this conversation and essentially relied on what they overheard. Under the Pilot's con, the first alteration of course to port was initiated using three degrees of port helm. At this time the vessel had a speed over ground (SOG) of nearly 18 knots. The initial helm order was followed by successive increases to five and then 10 degrees of rudder. About one minute after the initial three degree port helm order an offtrack alarm flashed on the ECDIS, but this information was not brought to the attention of the Master or the Pilot. The alarm appeared only as a visual indicator on the radar screen because its audio had been muted prior to the ship entering the channel. Even so, the Master and Pilot soon realised that the ship was proceeding dangerously close to a known rock shoal, so 20 degrees of port rudder was ordered, immediately followed by maximum port rudder. About three minutes after the initial helm order of three degrees, and despite the emergency helm order, the ship's bilge keel and the starboard propeller made contact with the rock as the ship passed. The ship was then navigated back to the centre of the channel and continued on its passage to port without further incident. The official report on this accident discusses the concept of allowing a ship to depart from an intended track in the belief that other influences, such as tide in this case, would return the ship to the intended track. The report notes that this carries a high risk when manoeuvring large ships in narrow waterways, where margins for error are small. The report posits that there is less risk when a ship is kept strictly to the intended track by increasing or decreasing its rate of turn in response to the external influences such as tide and wind. This method has the advantage of being unambiguous for other members of the bridge team tasked with monitoring the progress of the ship against the planned track. (Adapted from: https://steamshipmutual.com) It is possible to infer from the text that:

A)Both the one in charge of the ship and the Pilot saw eye-to-eye on the voyage planning at the outset.
B)The outer passenger ship was quite stationary.
C)Despite being highly manoeuvrable, the ship would have problems in changing direction very quickly in a very small space.
D)Due to a rock shoal the ship stranded.
E)The navigation lights were unlit, although the ship was keeping track of it.

EFOMM2021Dia 2Questao 5MatemáticaProgressõesMedia

Observe as progressões aritméticas a seguir e assinale a alternativa que representa o sexagésimo primeiro número a se repetir em ambas as progressões.

- 1, 3, 7, 11, 15, \dots

1, 4, 7, 10, \dots

A)301
B)399
C)619
D)727
E)799

EFOMM2021Dia 1Questao 5InglêsInterpretação de textoMedia

Passenger ship hits rock A passenger ship was inbound in daylight and fair visibility. The Master gave the Pilot a briefing regarding the ship's manoeuvring characteristics; the ship was highly manoeuvrable and would 'turn on a dime,' he said. The Master told the Pilot that a three-degree helm order would create a rate of turn of 10-15 degrees per minute. The bridge team would consist of the Pilot at the con while the Master would have overall navigational command. The staff captain would be in charge of communications while the first officer would be in charge of electronic navigation and collision avoidance. Finally, the second officer would be in charge of plotting the ship's position on the navigational chart. The Pilot and the Master discussed and agreed the intended passage plan, noting a strong flood tide that would be running astern. However, the subsequent investigation found that, due to miscommunication during the exchange, the passage inwards began with the Master and Pilot having different understandings of how the first turn would be conducted. The ship was lined up with the leading navigation lights and entered the channel without incident. As the Pilot took the con, the Master briefed the staff captain on the Master/ Pilot exchange and explained his understanding of how they were going to negotiate the turn to port. The rest of the bridge team were not included in this conversation and essentially relied on what they overheard. Under the Pilot's con, the first alteration of course to port was initiated using three degrees of port helm. At this time the vessel had a speed over ground (SOG) of nearly 18 knots. The initial helm order was followed by successive increases to five and then 10 degrees of rudder. About one minute after the initial three degree port helm order an offtrack alarm flashed on the ECDIS, but this information was not brought to the attention of the Master or the Pilot. The alarm appeared only as a visual indicator on the radar screen because its audio had been muted prior to the ship entering the channel. Even so, the Master and Pilot soon realised that the ship was proceeding dangerously close to a known rock shoal, so 20 degrees of port rudder was ordered, immediately followed by maximum port rudder. About three minutes after the initial helm order of three degrees, and despite the emergency helm order, the ship's bilge keel and the starboard propeller made contact with the rock as the ship passed. The ship was then navigated back to the centre of the channel and continued on its passage to port without further incident. The official report on this accident discusses the concept of allowing a ship to depart from an intended track in the belief that other influences, such as tide in this case, would return the ship to the intended track. The report notes that this carries a high risk when manoeuvring large ships in narrow waterways, where margins for error are small. The report posits that there is less risk when a ship is kept strictly to the intended track by increasing or decreasing its rate of turn in response to the external influences such as tide and wind. This method has the advantage of being unambiguous for other members of the bridge team tasked with monitoring the progress of the ship against the planned track. (Adapted from: https://steamshipmutual.com) Mark the option that is TRUE about the text.

A)As the Master does not hold ultimate command and responsibility on board, the Pilot and staff Captain take the navigation watch.
B)After taking over the navigational duties on the bridge, the Pilot gave instructions to the staff Captain on the Master/Pilot trade.
C)Both the Pilot and the Master took the offtrack alarm for granted as it went off the ECDIS.
D)The audible and visual emergency alarms had been hushed when the vessel entered the channel.
E)The Master as well as the Pilot found out that the vessel was running into risk and made up their minds to steer clear of it at once.

EFOMM2021Dia 2Questao 6MatemáticaAnálise combinatóriaFacil

Em uma turma de 50 alunos, 26 estão estudando Arquitetura Naval, 19 Inglês e 17 Cálculo. Sabe-se que dos alunos que estão estudando Arquitetura Naval, 6 estudam Inglês e 7 estudam Cálculo; e dos alunos que estão estudando Inglês, 9 estudam Cálculo. Além disso, há 6 alunos que não estão estudando essas três disciplinas. Quantos desses alunos que estão estudando Arquitetura Naval também estão estudando Inglês e Cálculo ao mesmo tempo?

A)0
B)4
C)7
D)9
E)10

EFOMM2021Dia 1Questao 6InglêsInterpretação de textoMedia

IMO, FAO to reduce marine plastic litter In light of the global issue of marine plastic litter, IMO and the Food and Agriculture Organization of the United Nations (FAO) shake their hands and inked an agreement in order to prevent and reduce marine plastic litter coming from shipping and fisheries. In fact, the agreement focuses on how the agencies will jointly execute the project and marks the next step towards many strategic partnerships anticipated under the project. Through their collaboration, both sides will move forward and jointly implement the GloLitter Partnerships Project, initially launched December 2019, with funding from Norway. For the records, the GloLitter project will help developing countries to identify opportunities to prevent and reduce marine litter, including plastic litter, from within the maritime transport and fishery sectors, and to decrease the use of plastics in these industries. "It will identify opportunities to re-use and recycle plastics. It will directly help to achieve one of the specific targets in the global Sustainable Development Goal (SDG) 14 - to prevent and significantly reduce marine pollution of all kinds, in particular from land-based activities, including marine debris and nutrient pollution, by 2025.", as IMO noted in its statement. Moreover, IMO and FAO will now reach out to their respective fields to strengthen cooperation, not least private sector participation through a Global Industry Alliance. The agreement was signed on 14 April 2020. (Adapted from: https://safety4sea.com) According to the text, it is possible to infer that:

A)IMO and the Food and Agriculture Organization of the United Nations made an agreement that would spur the jettison of waste in the oceans.
B)Marine pollution has been backed by some sectors of society.
C)The contract between IMO and FAO is related to the strategies for enlarging the provision of rubbish for the industries.
D)The contract will enable an ebb in marine pollution besides averting it.
E)The project is a helping hand in the development of other countries and a deterrent for recycling.

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